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provide solution for rd sharma maths class 12 chapter inverse trigonometric functions exercise 3.2 question 2

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Answer:\left [ \frac{-1}{2},\frac{1}{2} \right ]

Hint: Domain of (2x) lies in the interval [-1, 1].

Given: f(x) = 2\cos^{-1}2x +\sin^{-1}x


The domain of  \cos ^{-1}(2x) lies in the interval [-1, 1].

                     -1\leq 2x\leq 1

                      \frac{-1}{2}\leq x\leq \frac{1}{2}       

Domain of \cos ^{-1}(2x) is \frac{-1}{2}\leq x\leq \frac{1}{2}

Domain of \sin ^{-1}(x) is (-1,1)

Hence, domain of 2\cos^{-1}2x +\sin^{-1}x lies in the interval \left [ \frac{-1}{2},\frac{1}{2} \right ] .

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