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Explain Solution R.D.Sharma Class 12 Chapter 3 Inverse Trigonometric Function Exercise Multiple Choice Questions Question 34 maths Textbook Solution.

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Answer: [-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}]

Hint: The cos function interval is (-1, 1)

Given: Domain of \cos ^{-1}\left(x^{2}-4\right)


                The domain of \cos ^{-1}(x) \text { is }(-1,1)

    \begin{aligned} &\therefore-1 \leq x^{2}-4 \leq 1 \\ &\Rightarrow-1+4 \leq x^{2}-4+4 \leq 1+4 \\ &\Rightarrow 3 \leq x^{2} \leq 5 \\ &\Rightarrow \pm \sqrt{3} \leq x \leq \pm \sqrt{5} \\ &\Rightarrow x \in[-\sqrt{5},-\sqrt{3}] \cup[\sqrt{3}, \sqrt{5}] \end{aligned}

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