Question

Prove that tan(sin^-1 X)=x/✓1-x^2

Answer 1

Answer:

Step-by-step explanation:

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

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

Now,

$\sf{cos(\theta)=\sqrt{1-sin^{2}(\theta)}=\sqrt{1-x^2}}$

So,

$\sf{tan(\theta)=\dfrac{sin(\theta)}{cos(\theta)}=\dfrac{x}{\sqrt{1-x^2}}}$

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

$\sf{\implies\,tan\big(sin^{-1}(x)\big)=\dfrac{x}{\sqrt{1-x^2}}}$