Inverse Trigonometric Functions Question 177
Question: If $ {{\sin }^{-1}}\frac{x}{5}+cose{c^{-1}}( \frac{5}{4} )=\frac{\pi }{2}, $ then $ x= $
[EAMCET 1983; Karnataka CET 2004]
Options:
A) 4
B) 5
C) 1
D) 3
Show Answer
Answer:
Correct Answer: D
Solution:
$ {{\sin }^{-1}}\frac{x}{5}+cose{c^{-1}}\frac{5}{4}=\frac{\pi }{2}\Rightarrow {{\sin }^{-1}}\frac{x}{5}=\frac{\pi }{2}-cose{c^{-1}}\frac{5}{4} $
Therefore $ {{\sin }^{-1}}\frac{x}{5}=\frac{\pi }{2}-{{\sin }^{-1}}\frac{4}{5} $
Therefore $ {{\sin }^{-1}}\frac{x}{5}={{\cos }^{-1}}\frac{4}{5} $
Therefore $ {{\sin }^{-1}}( \frac{x}{5} )={{\sin }^{-1}}\frac{3}{5} $
Therefore $ x=3 $ .
BETA
