Question

What is tan(sin^-1(x/2))

Answer 1

Let

`\theta=\sin^(-1)\frac x2\implies\sin\theta=\frac x2`

Recall that

`\cos\theta=√(1-\sin^2\theta)=\sqrt{1-\frac{x^2}4}`

Then

`\tan\theta=(\sin\theta)/(\cos\theta)\implies\tan\left(\sin^(-1)\frac x2\right)=\frac{\frac x2}{\sqrt{1-\frac{x^2}4}}`

`\implies\tan\left(\sin^(-1)\frac x2\right)=\frac x{√(4-x^2)}`