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If cos^(-1)((1)/(sqrt(5)))=theta, then w...

If `cos^(-1)((1)/(sqrt(5)))=theta`, then what is the value of `"cosec"^(-1)(sqrt(5))` ?

A

`((pi)/(2))+theta`

B

`((pi)/(2))-theta`

C

`(pi)/(2)`

D

`-theta`

Text Solution

Verified by Experts

The correct Answer is:
B
Let, `cos^(-1)((1)/(sqrt(5)))= theta rArr cos theta = (1)/(sqrt(5))`
`rArr sec theta=sqrt(5) rArr sec^(-1)(sqrt(5))=theta`
`rArr (pi)/(2)-cosec^(-1)(sqrt(5))=theta" "(because sec^(-1)x + cosec^(-1)x = (pi)/(2))`
`rArr cosec^(-1)(sqrt(5))=(pi)/(2)-theta`
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