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If sinx+cosx=sqrt(y+1/y) for x in [0,pi]...

If `sinx+cosx=sqrt(y+1/y)` for `x in [0,pi]` , then (a) `x=pi/4` (b) `y=0` (c) `y=1` (d) `x=(3pi)/4`

A

`x=pi//4`

B

`y=0`

C

`y=1`

D

`x=3pi/4`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`y+1/y ge 2`
`rArr sqrt(y+1/y) ge sqrt(2)`
But `sin x+cos x le sqrt(2)`
`rArr y+1/y=2` and `sin x+cos x=sqrt(2)`
`rArr y=1` and `sin (x+pi/4)=1`
`rArr y=1` and `x=pi/4`
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