Inverse Trigonometric Functions Question 236
Question: If $ {{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}( \frac{12}{13} )={{\sin }^{-1}}C, $ then C =
[Pb. CET 1999]
Options:
A) $ \frac{65}{56} $
B) $ \frac{24}{65} $
C) $ \frac{16}{65} $
D) $ \frac{56}{65} $
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Answer:
Correct Answer: D
Solution:
Given $ {{\sin }^{-1}}C={{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}\frac{12}{13} $
$ \Rightarrow C=\sin ( {{\sin }^{-1}}\frac{3}{5}+{{\cos }^{-1}}\frac{12}{13} ) $ using, $ \sin (A+B)=\sin A\cos B+\cos A\sin B $
$ \Rightarrow C=\frac{3}{5}\times \frac{12}{13}+\sqrt{1-\frac{9}{25}}\sqrt{1-\frac{144}{169}} $
$ \Rightarrow C=\frac{56}{65} $ .
BETA
