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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 4 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 4 Maths Textbook Solution.

Answers (1)

Answer:
4
Given:
\sin^{-1}x+\sin^{-1}y+\sin^{-1}z+\sin^{-1}t= 2\pi \: then\, f\! ind\: x^{2}+y^{2}+z^{2}+t^{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},\sin^{-1}t\leq \frac{\pi }{2}
Solution:
\sin^{-1}x+\sin^{-1}y+\sin^{-1}z+\sin^{-1}t\leq 2\pi \: and\: it \: is\: given\: that \: L.H.S \: is\: 2\pi.
So\: it\: is\: possible\: only\: when
\sin^{-1}x= \frac{\pi }{2},\sin^{-1}y= \frac{\pi }{2},\sin^{-1}z= \frac{\pi }{2},\sin^{-1}t= \frac{\pi }{2}
x= 1,y= 1,z= 1,t= 1
  \therefore x^{2}+y^{2}+z^{2}+t^{2}= 4

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