## Simplifying Expressions With Trigonometric Functions of Inverse Trigonometric Functions

We can simplify expressions with sines and cosines of inverse trigonometric functions using substitutions.
To find
$sin(2 sin^{-1}x)$
substitute
$\theta = sin^{-1}x$
then
$sin(2 sin^{-1}x)=sin(2 \theta)=2 sin \theta cos \theta =2x \sqrt{1-x^2}$

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

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