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The number of distinct real roots of the...

The number of distinct real roots of the equation `sqrt(sin x)-(1)/(sqrt(sin x))=cos x("where" 0le x le 2pi)` is

A

1

B

2

C

3

D

more than 3

Text Solution

Verified by Experts

The correct Answer is:
B
`sqrt(sin x) - (1)/(sqrt(sin x))=cos x`
Squaring, `sin x-2+(1)/(sin x)=cos^(2)x`
`rArr sin x -2+(1)/(sin x)=cos^(2)x`
`rArr sin x-3 sin x +1 -sin^(3)x`
`rArr sin^(3)x+sin^(2)x-3 sin x + 1 =0`
`rArr (sin^(2)x+2 sin x-1)(sin x-1) =0`
`rArr sin x=1, sin x =-1 pm sqrt(2)`
`rArr x = pi//2, x=pi-sin^(-1)(-1+sqrt(2))` as (cos x must be lt 0)
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