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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 7 Trigonometric Ratios of Complementary Angles

Chapter 7 – Trigonometric Ratios of Complementary Angles Exercise Ex. 7

Question 1

Without using trigonometric tables, evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 1

(i)

                        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(ii)              

            R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(iii)

                        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(iv)

           R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(v)

           R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(vi)

           R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 2

Without using trigonometric tables, prove that:

(i)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(ii) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(iii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(iv)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(v)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(vi)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(vii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(viii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(ix)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 2

(i)                LHS = cos81° – sin9°

= cos(90° -9°)- sin9° = sin9° – sin9°

= 0 = RHS

(ii)              LHS = tan71° – cot19°

=tan(90° – 19°) – cot19° =cot19° – cot19°

=0 = RHS

(iii)               LHS = cosec80° – sec10°

= cosec(90° – 10°) – sec(10°)

= sec10° – sec10° = 0

= RHS

(iv)               LHS= R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(v)            R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(vi)             R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(vii)                 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary AnglesLHS = RHS

(viii) 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(ix)              LHS = (sin65° + cos25°) (sin65° – cos25°)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 3

Without
using trigonometric tables, prove that:

sin
53
cos37
+ cos53 sin37
= 1

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 4

cos
54
cos 36– sin 54
sin36
= 0

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 5

sec
70
sin 20
+ cos 20
cosec 70 = 2

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 6

sin
35
sin 55
– cos 35
cos 55
= 0

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 7

(sin
72
+ cos 18)(sin72
– cos18)
= 0

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 8

tan
48
tan 23
tan 42
tan 67
= 1

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 9

Prove
that:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 14

Prove
that:

sin
θ
cos (90
– θ)
+ sin (90
– θ) cos θ = 1

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 24

cos
1
cos2
cos3
… cos 180=
0

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 26

Prove that:

(i)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(ii) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(iii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(iv)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

(v)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 26

(i)                  LHS =

                    R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

= RHS

(ii)                LHS =

                   R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

= RHS

(iii)                  LHS =

                  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

= RHS

(iv)             LHS = cosec(65° + R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles) – sec(25°R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles ) – tan(55°R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles ) + cot(35° + R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles )

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

= RHS

(v)        LHS =

                 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

             = 0 + 1 = 1

             = RHS

Question 27

Express
each of the following in terms of T-ratios of angles lying between 0
and 45:

sin
67
+ cos 75

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 28

cot
65
+ tan 49

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 29

sec
78
+ cosec 56

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 30

cosec
54
+ sin 72

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 31

If A, B, C are the angles of a triangle ABC, prove that:R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 31

A + B + C = 180°

So, B + C= 180° – A

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 32

If
cos 2θ
= sin 4θ,
where 2θ
and 4θ
are acute angles, find the value of θ.

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 33

If
sec 2A= cosec (A – 42ᵒ), where 2A is an
acute angle, find the value of A.

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 34

If sin3A = cos(A – 26o), where 3A is an acute angle, find the value of A.

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 35

If tan 2A = cot(A – 12o), where 2A is an acute angle, find the value of A.

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 36

If sec 4A = cosec(A – 15o), where 4A is an acute angle, find the value of A.

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Question 37

Prove
that:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Trigonometric Ratios Of Complementary Angles

 

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