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Solve the following.
Evaluate: tan⁻¹(2cos(2sin⁻¹1/2)).
Evaluate: $\tan^{-1}\left(2\cos\left(2\sin^{-1}\dfrac{1}{2}\right)\right)$.
Answer
Answer
$\sin^{-1}\dfrac{1}{2} = \dfrac{\pi}{6}$, so $2\sin^{-1}\dfrac{1}{2} = \dfrac{\pi}{3}$ and $2\cos\dfrac{\pi}{3} = 2\cdot\dfrac{1}{2} = 1$.
$\tan^{-1}(1) = \dfrac{\pi}{4}$.