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Question
The value of cot (sin–1x) is ______.
Options
`sqrt(1 + x^2)/x`
`x/sqrt(1 + x^2)`
`1/x`
`sqrt(1 - x^2)/x`
Solution
The value of cot (sin–1x) is `sqrt(1 - x^2)/x`.
Explanation:
Let sin–1x = θ, then sin θ = x
⇒ cosec θ = `1/x`
⇒ cosec2θ = `1/x^2`
⇒ 1 + cot2θ = `1/x^2`
⇒ cot θ = `sqrt(1 - x^2)/x`.
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