Question

prove that tan^1 + cot^1x=π/2​

Answer 1

Answer:

Step-by-step explanation:

$\tt{Let\,\,\,tan^{-1}(x)=\,\theta}$

$\sf{\implies\,tan(\theta)=x}$

$\sf{\implies\,cot\bigg(\dfrac{\pi}{2}-\theta\bigg)=x}$

$\sf{\implies\,\dfrac{\pi}{2}-\theta=cot^{-1}(x)}$

$\sf{\implies\,cot^{-1}(x)=\dfrac{\pi}{2}-\theta}$

$\sf{\implies\,cot^{-1}(x)+\theta=\dfrac{\pi}{2}}$

$\sf{\implies\,cot^{-1}(x)+tan^{-1}(x)=\dfrac{\pi}{2}}$