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If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,...

If `2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi),` then the value of `alpha+beta` is (a)`(3pi)/4` (b) `pi` (c) `(3pi)/2` (d) `(5pi)/4`

A

`(3pi)/(4)`

B

`pi`

C

`(3pi)/(2)`

D

`(5pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
`2|sin2alpha|le2`
and `|tan beta+cot beta|=(1)/(|sin beta cos beta|)=2|co sec2beta|ge2`
`therefore 2|sin2alpha|=|tan beta+cotbeta|=2`
`therefore alpha=beta=(3pi)/(4)`
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