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If 2 sin 2alpha= | tan beta+ cot beta |a...

If `2 sin 2alpha= | tan beta+ cot beta |alpha,beta, in((pi)/(2),pi)`, then the value of `alpha+beta` is

A

`(3pi)/(4)`

B

`pi`

C

`(3pi)/(2)`

D

`(5pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
It is true when `x=(pi)/(2),y=(pi)/(4)`
`tan y=1rArr(2tan((y)/(2)))/(1-tan^(2)((y)/(2)))=1`
`rArr tan^(2)((y)/(2))+2tan((y)/(2))=1`
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