Question

tan(2sin^-1x). Write the expression as an algebraic expression in x (without trig or inverse trig functions)

Answer 1

\[\text {Let} \theta = \sin^{-1} x\]
\[\sin \theta = x \]
now goal is to find
\[\tan 2 \theta\]
\[\rightarrow \tan 2 \theta = \frac{\sin 2\theta}{\cos 2 \theta} = \frac{2 \sin \theta \cos \theta}{\cos^2 \theta - \sin^2 \theta}\]
Find cos using pythagorean identity
\[\cos \theta = \sqrt{1-x^2}\]
plug in the values and you are done