WBJEE · Maths · Inverse Trigonometric Functions
If \(\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2},\) then the value of \(x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}\) is equal to
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
We know that \(\left|\sin ^{-1} x\right| \leq \frac{\pi}{2}\) Hence, from the given relation we observe that each of \(\sin ^{-1} x, \sin ^{-1} y\) and \(\sin ^{-1} x\) will be \(\frac{\pi}{2}\) so that \(x=y=x=\sin \frac{\pi}{2}=1\)…
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