First slide

Properties of ITF

Question

$If \sin^{- 1} x + \sin^{- 1} y + \sin^{- 1} z = \frac{3 π}{2}$ then the value of $x^{100} + y^{100} + z^{100} - \frac{3}{x^{101} + y^{101} + z^{101}}$ is

Easy

A

0
B

1
C

2
D

3

Solution

We have sin^–1x + sin^–1y + sin^–1z = $\frac{3 π}{2}$ it is possible only when
$\begin{array}{l} \sin^{- 1} x = \frac{π}{2} \Rightarrow x = 1 ∵ \sin^{- 1} x \leq \frac{π}{2} \\ \sin^{- 1} y = \frac{π}{2} \Rightarrow y = 1; \sin^{- 1} z = \frac{π}{2} \Rightarrow z = 1 \\ ∴ x^{100} + y^{100} + z^{100} - \frac{3}{x^{101} + y^{101} + z^{101}} \\ = 1 + 1 + 1 - \frac{3}{3} = 3 - 1 = 2 \end{array}$

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