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If cot^(-1)(-1/5)=x then sinx=?...

If `cot^(-1)(-1/5)=x` then `sinx=?`

A

`1/sqrt(26)`

B

`5/sqrt(26)`

C

`1/sqrt(24)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`cot^(-1)(-1/5) = x rArr cotx=-1/5`, where `x in (0,pi)`.
`sinx gt 0` in `(0,pi)`.
`sinx=1/("cosec"x)=1/sqrt(1+cot^(2)x)=1/sqrt(1+1/25)=5/sqrt(26)`.
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