Inverse Trigonometric Functions Question 94
Question: If the equation $ {{(si{n^{-1}}x)}^{3}}+{{(co{s^{-1}}x)}^{3}}=a{{\pi }^{2}} $ has no real root then
Options:
A) $ a>0 $
B) $ a<\frac{1}{32} $
C) $ a<3 $
D) None of these
Show Answer
Answer:
Correct Answer: B
$ {{(si{n^{-1}}x)}^{3}}+{{(co{s^{-1}}x)}^{3}} $
$ =\frac{\pi }{2}[ {{( \frac{\pi }{2} )}^{2}}-3{{\sin }^{-1}}x{{\cos }^{-1}}x ] $
$ =\frac{3\pi }{2}[ {{(si{n^{-1}}x-\frac{\pi }{4})}^{2}}+\frac{{{\pi }^{2}}}{48} ] $
BETA
