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Question: cos<sup>–1</sup>\(\left\{ \frac{1}{2}x^{2} + \sqrt{1–x^{2}}\sqrt{1–\frac{x^{2}}{4}} \right\}\)=cos<s...

cos–1{12x2+1–x21–x24}\left\{ \frac{1}{2}x^{2} + \sqrt{1–x^{2}}\sqrt{1–\frac{x^{2}}{4}} \right\}=cos–1x2\frac{x}{2}–cos–1x holds if –

A

|x| £ 1

B

x Î R

C

0 £ x £ 1

D

– 1 £ x £ 0

Answer

0 £ x £ 1

Explanation

Solution

RHS : cos–1 x2\frac{x}{2} – cos–12

cos–1{12x2+1–x21–x24}\left\{ \frac{1}{2}x^{2} + \sqrt{1–x^{2}}\sqrt{1–\frac{x^{2}}{4}} \right\}

considering cos–1x2\frac{x}{2} ³ cos–1x ̃ x2\frac{x}{2}£ x

True for all positive x also for cos–1x – 1£ x £ 1

Hence : 0 £ x £ 1