Inverse Trigonometric Functions Question 213
Question: If $ a<\frac{1}{32}, $ then the number of solution of $ {{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}=a{{\pi }^{3}} $ is
Options:
A) 0
B) 1
C) 2
D) Infinite
Show Answer
Answer:
Correct Answer: A
Solution:
From previous solution $ \frac{{{\pi }^{3}}}{32}\le {{({{\sin }^{-1}}x)}^{3}}+{{({{\cos }^{-1}}x)}^{3}}\le \frac{7\pi }{8} $
Here $ a<\frac{1}{32} $ .
So, number of solution is zero.
BETA
