Inverse Trigonometric Functions Question 152
Question: $ {{\tan }^{-1}}\frac{x}{\sqrt{a^{2}-x^{2}}}= $
Options:
A) $ \frac{1}{a}{{\sin }^{-1}}( \frac{x}{a} ) $
B) $ a{{\sin }^{-1}}( \frac{x}{a} ) $
C) $ {{\sin }^{-1}}( \frac{x}{a} ) $
D) $ {{\sin }^{-1}}( \frac{a}{x} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\tan }^{-1}}\frac{x}{\sqrt{a^{2}-x^{2}}}={{\tan }^{-1}}( \frac{a\sin \theta }{a\cos \theta } ) $ (Putting $ x=a\sin \theta ) $
$ ={{\tan }^{-1}}(\tan \theta )=\theta ={{\sin }^{-1}}( \frac{x}{a} ) $ .
BETA
