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If cottheta=2 costheta , where (pi//2)lt...

If `cottheta=2 costheta` , where `(pi//2)ltthetaltpi` , then what is the value of `theta` ?

A

`5pi//6`

B

`2pi//3`

C

`3pi//4`

D

`11pi//12`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `cottheta=2costheta,(pi)/(2)ltthetaltpi`
`rArr(costheta)/(sin theta)=2costhetarArr(costheta)/((2costheta))=sintheta`
`rArr(1)/(2)=sinthetarArr"sin"(pi)/(6)=sinthetarArrtheta=(pi)/(6)`
But `(pi)/(2)ltthetaltpithereforethetapi-(pi)/(6)=(5pi)/(6)`
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