Question

In the integral
`int(cos 8x+1)/(cot 2x-tan 2x)dx=A cos 8x+k`, where k is an arbitrary constant,then A is equal to
A. `-(1)/(16)`
B. `(1)/(16)`
C. `(1)/(8)`
D. `-(1)/(8)`

Answer 1

Correct Answer - A
`LHS=int(2cos^(2)4x)/((cos^(2)2x-sin^(2)2x)/(cos2xsin2x))dx`
`=int(2cos^(2)4x xx cos 2x sin2x)/(cos 4x)dx`
`=intcos4x xx sin 4x dx =(1)/(2)int sin8x dx`
`=(-1)/(2)(cos8x)/(8)+k=-(1)/(16)cos 8x+k`
then `A=-(1)/(16)`