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Question: cos<sup>–1</sup> \(\left\{ \frac { 1 } { 2 } x ^ { 2 } + \sqrt { 1 - x ^ { 2 } } \sqrt { 1 - \frac {...

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

A

|x| £ 1

B

x Ī R

C

0 £ x £ 1

D

–1 £ x £ 0

Answer

0 £ x £ 1

Explanation

Solution

RHS cos–1 – cos–1 x; cos–1

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

true for all positive x, also

for cos–1 x ® –1 £ x £ 1,Hence 0 £ x £ 1