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The range of 'y, such that the equation ...

The range of 'y, such that the equation in x, `y + cos x = sin x` has a real solution is

A

`[-2, 2]`

B

`[- sqrt(2), sqrt(2)]`

C

`[-1, 1]`

D

`[-1//2, 1//2]`

Text Solution

Verified by Experts

The correct Answer is:
B
`y= sinx - cos x = sqrt(2) [1/sqrt(2) sin x -1/sqrt(2) cos x]`
`=sqrt(2) sin (x-pi/4)`
`rArr -sqrt(2) le y le sqrt(2)`
`rArr` Range od y is `[-sqrt(2), sqrt(2)]`
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CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
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