`If"sin"{cot^(-1)(x+1)}="cos"(tan^(-1)x),` then find `xdot`

Answer

`x=-frac{1}{2}`

Explanation

`L.H.S=sin [cot ^{-1}(x+1)]`

` Let , cot ^{-1}(x+1)=A Rightarrow cot A=x+1`

`cot ^{2} A=(x+1)^{2} `

`{cosec}^{2} A-1=(x+1)^{2}`

`{cosec}^{2} A=1+(x+1)^{2}`

`{cosec} A=sqrt{1+(x+1)^{2}}`

`sin A=frac{1}{sqrt{1+(x+1)^{2}}} `


`therefore L. H.S=sin [cot ^{-1}(x+1)]
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