Question

`int(dx)/(cos(2x)cos(4x))=`
A. `(1)/(2sqrt2)log|(1+sqrt2sin2x)/(1-sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`
B. `(1)/(2sqrt2)log|(1-sqrt2sin2x)/(1+sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`
C. `(1)/(sqrt2)log|(1+sqrt2sin2x)/(1-sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`
D. none of these

Answer 1

Correct Answer - B
`int(sin(4x-2x)dx)/(sin(2x)cos(2x)cos(4x))`
`=int(sin(4x)dx)/(sin(2x)cos(4x))-int sec2xdx`
`=2int(cos2xdx)/(cos4x)-(1)/(2)(log|sec 2x-tan 2x|)`
`=2int(cos2xdx)/(1-2sin^(2)2x)-(1)/(2)(log|sec2x-tan2x|)`
`=int(dt)/(1-2t^(2))-(1)/(2)(log|sec 2x-tan2x|)`