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Trigonometry
Simplifying Expressions With Trigonometric Functions of Inverse Trigonometric Functions
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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