Mathematics - Trigonometric Equation Question with Solution | TestHub

$\sin \left({\cot }^{-1}(1+x)\right)=\cos \left({\tan }^{-1}x\right)$ $\begin{array}{rl}& \Rightarrow {\mathrm{cosec}}^2\left({\cot }^{-1}(1+x)\right)={\sec }^2\left({\tan }^{-1}x\right)\\ & \Rightarrow 1+{\left[\cot \left({\cot }^{-1}(1+x)\right)\right]}^2\\ & \Rightarrow =1+{\left[\sec \left({\tan }^{-1}x\right)\right]}^2\\ & \Rightarrow (1+x{)}^2=x^2\Rightarrow x=-\frac{1}{2}\end{array}$