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If cosectheta=(p+q)/(p-q),then cot(pi,//...

If `cosectheta=(p+q)/(p-q),then cot(pi,//4+theta//2)=`

A

`sqrt((p)/(q))`

B

`sqrt((q)/(p))`

C

`sqrt(pq)`

D

pq

Text Solution

Verified by Experts

The correct Answer is:
B
`cosec. Theta =(p+1)/(p-q)rArr (1)/(sin theta) = (p+q)/(p-q)`
Apply componendo and dividendo
`(1+sin theta)/(1-sin theta)=(p+q+p-q)/(p+q-p+q)`
`rArr {(cos.(theta)/(2)+sin.(theta)/(2))/(cos.(theta)/(2)-sin.(theta)/(2))}^(2)=(p)/(q)`
`rArr {(1+tan.(theta)/(2))/(1-tan.(theta)/(2))}^(2)=(p)/(q)`
`rArr tan^(2)((pi)/(4)+(theta)/(2))=(p)/(q)`
`rArr cot^(2)((pi)/(4)+(theta)/(2))=(q)/(p)`
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