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Question

Mathematics Question on Inverse Trigonometric Functions

sin\left\\{2\,cos^{-1}\left(- \frac{3}{5}\right)\right\\} is equal to

A

625\frac{6}{25}

B

2425\frac{24}{25}

C

45\frac{4}{5}

D

−2425-\frac{24}{25}

Answer

−2425-\frac{24}{25}

Explanation

Solution

sin\left\\{2\,cos^{-1}\left(- \frac{3}{5}\right)\right\\} = 2\,sin\left\\{cos^{-1}\left(- \frac{3}{5}\right)\right\\}cos\left\\{cos^{-1}\left(- \frac{3}{5}\right)\right\\} = 2\,sin\left\\{\pi - cos^{-1} \frac{3}{5}\right\\}\times \left(-\frac{3}{5}\right) = -\frac{6}{5}sin\left\\{cos^{-1} \frac{3}{5}\right\\} =−65sin(sin−11−925)= -\frac{6}{5}sin\left(sin^{-1}\sqrt{1-\frac{9}{25}}\right) =−65×45=−2425 = -\frac{6}{5} \times \frac{4}{5} = -\frac{24}{25}