Inverse Trigonometric Functions Question 229
Question: If $ {{\cos }^{-1}}\frac{3}{5}-{{\sin }^{-1}}\frac{4}{5}={{\cos }^{-1}}x, $ then x =
[AMU 1978]
Options:
A) 0
B) 1
C) -1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{\cos }^{-1}}\frac{3}{5}-{{\sin }^{-1}}\frac{4}{5}={{\cos }^{-1}}x $
$ \Rightarrow {{\cos }^{-1}}\frac{3}{5}-{{\cos }^{-1}}\sqrt{1-\frac{16}{25}}={{\cos }^{-1}}x $
$ \Rightarrow {{\cos }^{-1}}\frac{3}{5}-{{\cos }^{-1}}\frac{3}{5}={{\cos }^{-1}}x $
$ \Rightarrow {{\cos }^{-1}}x=0\Rightarrow x=1 $ .
BETA
