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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 5 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 5 Maths Textbook Solution.

Answers (1)

Answer:
3
Given:
\left ( \sin^{-1}x \right )^{2}+\left (\sin^{-1}y \right )^{2}+\left ( \sin^{-1}z \right )^{2}= \frac{3}{4}\pi ^{2} \,\, then\, find \,\, x^{2}+y^{2}+z^{2}.
Hint:
We\, know\, that \, the\, range\, o\! f \, \sin^{-1} is \left [ \frac{-\pi }{2} ,\frac{\pi }{2}\right ]
\sin^{-1}x\leq \frac{\pi }{2},\sin^{-1}y \leq \frac{\pi}{2}, \sin^{-1}z\leq \frac{\pi}{2}
\left ( \sin^{-1}x \right )^{2}\leq \frac{\pi ^{2}}{4},\left (\sin^{-1}y \right )^{2}\leq \frac{\pi ^{2}}{4},\left ( \sin^{-1}z \right )^{2}\leq \frac{\pi ^{2}}{4}
\left ( \sin^{-1}x \right )^{2}+\left (\sin^{-1}y \right )^{2}+\left ( \sin^{-1}z \right )^{2}\leq \frac{3}{4}\pi ^{2} \, \, and \, it\, is\, given\, that\, L.H.S\, is \,\, \frac{3}{4}\pi ^{2}.
So\: it\: is\: possible\: only\: when
\sin^{-1}x= \frac{\pi }{2},\sin^{-1}y= \frac{\pi}{2}, \sin^{-1}z= \frac{\pi}{2}
x= 1,y= 1,z= 1
\therefore x^{2}+y^{2}+z^{2}= 3

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