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The value of sectheta/sqrt(1+tan^2theta...

The value of `sectheta/sqrt(1+tan^2theta)+(cosectheta)/(sqrt(1+cot^2theta))" for "theta in (pi,(3pi)/2)` is

A

0

B

-2

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`sectheta/sqrt(1+tan^2theta)+(cosectheta)/sqrt(1+cot^2theta),theta in(pi,3pi//2)`
`=secthetaabscostheta+cosecthetaabssintheta`
`=sectheta(-costheta)+cosectheta(-sintheta) [As thetain(pi,3pi//2)]`
`=-1-1`
`=-2`
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