If $x = \tan^{- 1} (1) + \cos^{- 1} (- 1 / 2) + \sin^{- 1} (- 1 / 2)$ and $y = \cos [1 / 2 \cos^{- 1} (1 / 8)],$ then

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y=3px

x=py

y = px

x=2py

answer is C.

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Detailed Solution

$x = \frac{π}{4} + \frac{π}{2} = 3 \frac{π}{4} let \cos^{- 1} \frac{1}{8} = θ \Rightarrow \cos θ = \frac{1}{8} y = \cos \frac{θ}{2} = \sqrt{\frac{1 + cosθ}{2}} = \sqrt{\frac{1 + \frac{1}{8}}{2}} = \frac{3}{4} \frac{x}{y} = π$

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