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If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y...

If `cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y+1/y),(x y >0); x , y ,alpha,beta in R` then `sin(alpha+beta+gamma+singammaAAgamma in R` `cosalphacosbeta=1AAalpha,beta in R` `(cosalpha+cosbeta)^2=4AAalpha,beta in R` `sin(alpha+beta+gamma)=sinalpha+sinbeta+s ingammaAAa , b ,gamma in R`

A

`sin(alpha+beta+gamma)=singammaAAgammainR`

B

`cosalphacosbeta=1AAalpha,beta inR`

C

`(cosalpha+cosbeta)^2=4AAalpha,beta in R`

D

`sin (alpha+beta+gamma)=sinalpha+sinbeta+singammaAAa,b,gammainR`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`cosalpha=1/2(x+1/x)andcosbeta=1/2(y+1/y)`
since `xygt0`,we have
`x+1/2ge2orle-2andy+1/yge2orle-2`
`rArrcosalpha=1,cosbeta=1`
`or cosalpha=-1,cosbeta=-1`
`:. cosalphacosbeta=1`
`rArralpha+beta" is an even multiple of " pi`
`(cosalpha+cosbeta)^2=4`
`rArr sin(alpha+beta+gamma)=sin(2npi+gamma)=singamma`
Also, `sinalpha=sinbeta=0`
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