If 12< x < 1 then Cos-1x + Cos-1x+1-x22=

Cos-1 x + Cos-1 x . 12+ 121-x2= Cos-1 x + Cos-1 12-Cos-1x=π4

If 12< x < 1 then Cos-1x + Cos-1x+1-x22=

Cos-1 x + Cos-1 x . 12+ 121-x2= Cos-1 x + Cos-1 12-Cos-1x=π4

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If $\frac{1}{\sqrt{2}} < x < 1$ then ${Cos}^{- 1} x + {Cos}^{- 1} (\frac{x + \sqrt{1 - x^{2}}}{\sqrt{2}}) =$

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${2 Cos}^{-1} x - \frac{π}{4}$

${2 Cos}^{-1} x$

$\frac{π}{4}$

answer is C.

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Detailed Solution

${Cos}^{-1} {x + Cos}^{-1} (x . \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} \sqrt{{1-x}^{2}})$

${= Cos}^{-1} {x + Cos}^{-1} (\frac{1}{\sqrt{2}}) {-Cos}^{-1} x= \frac{π}{4}$

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If 12< x < 1 then Cos-1x + Cos-1x+1-x22=

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If $\frac{1}{\sqrt{2}} < x < 1$ then ${Cos}^{- 1} x + {Cos}^{- 1} (\frac{x + \sqrt{1 - x^{2}}}{\sqrt{2}}) =$