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If $(\cos α, \cos β)$ are the new co-ordinates of a point P when the axes are translated to the point (1, 1) then the original coordinates are

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$(2 \cos^{2} \frac{α}{2}, 2 \cos^{2} \frac{β}{2})$

$(2 \cos^{2} \frac{α}{2}, 2 \sin^{2} \frac{β}{2})$

$(2 \sin^{2} \frac{α}{2}, 2 \cos^{2} \frac{β}{2})$

$(- 2 \cos^{2} \frac{α}{2}, 2 \cos^{2} \frac{β}{2})$

answer is A.

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Detailed Solution

$\begin{array}{l} x = X + h = 1 + \cos α = 2 \cos^{2} \frac{α}{2} \\ y = Y + k = 1 + \cos β = 2 \cos^{2} \frac{β}{2} \end{array}$

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