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The number of real solutions of the equa...

The number of real solutions of the equation
`sqrt(1+cos2x) = sqrt(2)cos^(-1)(cosx)` in `[pi/2,pi]` is

A

0

B

1

C

2

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `sqrt(1+cos2x)=sqrt(2)cos^(-1)(cosx)`
` thereforesqrt(2cos^(2)x)=sqrt(2)x`
`rArrsqrt(2)|cosx|=sqrt(2)x`
For `X in[(pi)/(2),pi],|cosx|=-cosx`
`-sqrt(2)cosx=sqrt(2)xrArr-cosx=x`
`thereforecosx=-x`
Hence , no solution exist.
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