MHT CET · Maths · Inverse Trigonometric Functions
With reference to the principal values, if \(\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}\), then \(x^{100}+y^{100}+z^{100}=\)
- A 2
- B 3
- C 1
- D 6
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\(\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}=\frac{\pi}{2}+\frac{\pi}{2}+\frac{\pi}{2}=\sin ^{-1}\) \((1)+\sin ^{-1}(1)+\sin ^{-1}(1) \)
\( \Rightarrow x=y=z=1 \)
\( \Rightarrow x^{100}+y^{100}+z^{100}=1^{100}+1^{100}+1^{100}=3\)
\( \Rightarrow x=y=z=1 \)
\( \Rightarrow x^{100}+y^{100}+z^{100}=1^{100}+1^{100}+1^{100}=3\)
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