# NCERT solution class 12 chapter 1 Integrals exercise 1.3 mathematics part 2

## EXERCISE 1.3

#### Question 2:

It is known that,

#### Question 3:

cos 2x cos 4x cos 6x

It is known that,

sin3 (2x + 1)

Let

sin3 x cos3 x

#### Question 6:

sin x sin 2x sin 3x

It is known that,

#### Question 7:

sin 4x sin 8x

It is known that,

sin A . sin B = 12cosA-B-cosA+B∴∫sin4x sin8x dx=∫12cos4x-8x-cos4x+8xdx=12∫cos-4x-cos12xdx=12∫cos4x-cos12xdx=12sin4x4-sin12x12+C

sin4 x

cos4 2x

#### Question 16:

tan4x

From equation (1), we obtain

#### Question 19:

1sinxcos3x=sin2x+cos2xsinxcos3x=sinxcos3x+1sinxcosx

⇒1sinxcos3x=tanxsec2x+1cos2xsinxcosxcos2x=tanxsec2x+sec2xtanx

#### Question 21:

sin−1 (cos x)

It is known that,

Substituting in equation (1), we obtain

#### Question 23:

is equal to

A. tan x + cot x + C

B. tan x + cosec x + C

C. − tan x + cot x + C

D. tan x + sec x + C

Hence, the correct answer is A.

#### Question 24:

equals

A. âˆ’ cot (exx) + C

B. tan (xex) + C

C. tan (ex) + C

D. cot (ex) + C