The total number of solution of `cosx=sqrt(1-sin2x)` in `[0,2pi]` is equal to 2 (b) 3 (c) 5 (d) none of these

Options

A. 2
B. 3
C. 5
D. none of these

Answer

B

Explanation

`cos x=sqrt(1- sin 2x)=|sin x-cos x|`
(a) `sin x lt cos x`
`rArr x in [0, pi/4) uu ((5pi)/4, 2pi]` ...(i)
Then the given equation is
`cos x = cos x - sin x`
or `sin x=0`
`rArr x=2pi` [ from Eq. (i)]
(b) `sin x ge cos x`
`rArr x in (pi/4, (5pi)/4)`
`rArr cos x=sin x-cos x`
or `tan x=2`
`rArr x=tan^(1-) 2` ...(ii)
Hence, there are two solutions.