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If $x = \tan^{- 1} (1) + \cos^{- 1} (- \frac{1}{2}) + \sin^{- 1} (- \frac{1}{2})$ $a n d$ $y = \cos (\frac{1}{2} \cos^{- 1} \frac{1}{8})$ $t h e n$

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Correct option is C

We have x=tan-11+cos-1-12+sin-1-12 =π4+π2 =3π4 Let cos-118=α. Then cosα=18. Now y=cos12cos-118 =cosα2 =1+cosα2 =1+182 =34 ∴x=3π4=πy

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If x=tan−11+cos−1-12+sin−1-12 and y=cos12cos-118 then

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If $x = \tan^{- 1} (1) + \cos^{- 1} (- \frac{1}{2}) + \sin^{- 1} (- \frac{1}{2})$ $a n d$ $y = \cos (\frac{1}{2} \cos^{- 1} \frac{1}{8})$ $t h e n$