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sin(cot^(-1)(tan(cos^(-1)x))) is equal t...

`sin(cot^(-1)(tan(cos^(-1)x)))` is equal to a) `x` b) `sqrt(1-x^2)` c) `1/x` d) none of these

Text Solution

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Put `cos^(−1)x=θ `
∴`x=cosθ`
∴`tanθ=sqrt(1−x^2)/x`
∴`tan(cos^(−1)x)=tanθ=sqrt(1−x^2)/x`
​​ ∴`cot^(−1)(tan(cos^(−1)))=cot^(−1)(sqrt(1−x^2)/x)=ϕ `(say) ...
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    D
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