Inverse Trigonometric Functions Question 5
Question: The value of $ \tan [ {{\sin }^{-1}}( \frac{3}{5} )+{{\cos }^{-1}}( \frac{3}{\sqrt{13}} ) ] $ is
[AMU 2001]
Options:
A) $ \frac{6}{17} $
B) $ \frac{6}{\sqrt{13}} $
C) $ \frac{\sqrt{13}}{5} $
D) $ \frac{17}{6} $
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Answer:
Correct Answer: D
Solution:
$ \tan [ {{\sin }^{-1}}( \frac{3}{5} )+{{\cos }^{-1}}( \frac{3}{\sqrt{13}} ) ] $ = $ \tan ( {{\tan }^{-1}}\frac{3}{4}+{{\tan }^{-1}}\frac{2}{3} ) $ = $ \tan ( {{\tan }^{-1}}\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}} ) $ = $ \tan [ {{\tan }^{-1}}\frac{17}{12}\times \frac{12}{6} ] $ = $ \frac{17}{6} $ .
BETA
