Question

sin'x + sin'1/x +cos'1/x + cos'1/x is equal to
​

Answer 1

Step-by-step explanation:

Let [math]\theta = \sin^{-1}(x) \implies x = \sin(\theta)[/math]

[math]\cos^{-1}(x) = \cos^{-1} (\sin \theta) = \cos^{-1} (\cos (\dfrac{\pi}{2} - \theta) ) = \dfrac{\pi}{2} - \theta[/math]

[math]\sin^{-1}(x) + \cos^{-1}(x) = \theta + \dfrac{\pi}{2} - \theta = \dfrac{\pi}{2}[/math]

Ans: [math]\dfrac{\pi}{2}[/math]