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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 3 Subquestion (iv) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.1 Question 3 Subquestion (iv) Maths Textbook Solution.

Answers (1)

Answer:
\left [ \frac{-1}{2} ,\frac{1}2{}\right ]
Hint:
The \, domain\, o\! f \sin^{-1}x \, is \left [ -1,1 \right ].
Given:
f\! \left ( x \right )= \sin^{-1}x+\sin^{-1}2x
Explanation:
Now, we\, f\! ind\, the\, domain\, o\! f \sin^{-1}2x
-1\leq 2x\leq 1
\frac{-1}{2}\leq x\leq \frac{1}{2}
The\, domain\, o\! f \, f\! \left ( x \right ) is\, the\, inter\! section \, o\! f\, domains\, o\! f \sin^{-1}x\, and \, \sin^{-1}2x.
    \left [ \frac{-1}2,\frac{1}2{}{} \right ]\cap \left [ -1,1 \right ]           
= \left [ \frac{-1}2,\frac{1}2{}{} \right ]
Hence, the\, domain\, o\! f \sin^{-1}x+\sin^{-1}2x \, is = \left [ \frac{-1}2,\frac{1}2{}{} \right ].

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