Question

Let ${\sin }^{-1}x=\theta$ then the value of $cose{c}^{-1}\frac{1}{\sqrt{1-x^2}}$.

Answer 1

Given, ${\sin }^{-1}x=\theta$

or, $\sin \theta =x$

or, $\cos \theta =\sqrt{1-x^2}$

or, $\sec \theta =\frac{1}{\sqrt{1-x^2}}$

or, $cosec({90}^o-\theta )=\frac{1}{\sqrt{1-x^2}}$

or, $\frac{\pi }{2}-\theta =cose{c}^{-1}\frac{1}{\sqrt{1-x^2}}$.