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if 2sec2alpha=tanbeta+cotbeta then one o...

if `2sec2alpha=tanbeta+cotbeta` then one of the value of alpha+beta is

A

`(pi)/(4)`

B

`(pi)/(2)`

C

`pi`

D

`npi-(pi)/(4),ninI`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `2sec2alpha=tanbeta+cotbeta`
`rArr2sec2alpha=(1+tan^(2)beta)/(tanbeta)=(sec^(2)beta)/(tanbeta)`
`=(2)/(2cosbeta*sinbeta)=2cosec2beta`
`thereforesec2alpha=sec((pi)/(2)-2beta)`
`rArrcos2alpha=cos((pi)/(2)-2beta)`
`rArrcos2alpha=cos((pi)/(2)-2beta)`
`rArr2alpha=2npi+-((pi)/(2)-2beta)`
Taking +ve sign ,we have
`2(alpha+beta)=2npi+(pi)/(2)`
`rArralpha+beta-npi+(pi)/(4),AAninZ`
For `n=0,alpha+beta=(pi)/(4)`
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