JEE Advance - Mathematics (2002 - No. 18)
Let $$0 < \alpha < {\pi \over 2}$$ be fixed angle. If $$P = \left( {\cos \theta ,\,\sin \theta } \right)$$ and $$Q = \left( {\cos \left( {\alpha - \theta } \right),\,\sin \left( {\alpha - \theta } \right)} \right),$$ then $$Q$$ is obtained from $$P$$ by
clockwise rotation around origin through an angle $$\alpha $$
anticlockwise rotation around origin through an angle $$\alpha $$
reflection in the line through origin with slope tan $$\alpha $$
reflection in the line through origin with slope tan $$\left( {\alpha /2} \right)$$
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