Inverse Trigonometric Functions Question 47
Question: $ \sin
[ 3{{\sin }^{-1}}( \frac{1}{5} ) ]= $ [Kerala (Engg.) 2005]
Options:
A) 71/125
B) 74/125
C) 3/5
D) 1/2
Show Answer
Answer:
Correct Answer: A
Solution:
$ \sin [ 3{{\sin }^{-1}}\frac{1}{5} ] $
$ =\sin [ {{\sin }^{-1}}{ 3( \frac{1}{5} )-4{{( \frac{1}{5} )}^{3}} } ] $
$ =\sin [ {{\sin }^{-1}}{ \frac{3}{5}-\frac{4}{125} } ] $
$ =\sin [ {{\sin }^{-1}}( \frac{75-4}{125} ) ] $
$ =\sin [ {{\sin }^{-1}}\frac{71}{125} ]=\frac{71}{125} $ .
BETA
