Number of solutions of the equation `sin x + cos x-2sqrt(2) sin x cos x=0` for `x in [0, pi]` is

Options

A. 3
B. 0
C. 1
D. 2

Answer

D

Explanation

`sin x + cos x - 2 sqrt(2) sin x cos x=0`
`rArr sin x+cos x=2sqrt(2) sin x cos x`
`rArr 1+sin 2x=2 sin^(2) 2x`
`rArr 2 sin^(@) 2x- sin 2x-1=0`
`rArr (2 sin 2x+1) (sin 2x-1)=0`
`rArr sin 2x=-1//2 or sin 2x=1`
`rArr 2x=11 pi//6, pi//2`
`rArr x=11pi//12, pi//4`