If `2sin^2((pi/2)cos^2x)=1-cos(pis in2x),x!=(2n+1)pi/2,n in I ,` then `cos2x` is equal to `1/5` (b) `3/5` (c) `4/5` (d) `1`

Options

A. `1//5`
B. `3//5`
C. `4//5`
D. `1`

Answer

B

Explanation

The given equation is equivalent to
`2 sin^(2) ((pi//2) cos^(2) x)=2 sin^(2) ((pi//2) sin 2x)`
or `cos^(2) x= sin 2x`
or `cos x (cos x -2 sin x)=0`
`rArr 1-2 tan x=0` as `cos x ne0, x ne (2n+1) pi/2`
or `tan x=1/2`
`rArr cos 2x=(1-tan^(2) x)/(1+tan^(2) x)=3/5`