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Question

Let 0<α<π2 be a fixed angle. If P=(cosθ,sinθ) and Q=(cos(αθ),sin(αθ)), then Q is obtained from P by?
  1. Clockwise rotation around origin through an angle α
  2. Anti-clockwise rotation around origin through an angle α
  3. Reflection in the line through origin with slope tanα
  4. Reflection in the line through origin with slope tanα/2

A
Clockwise rotation around origin through an angle α
B
Anti-clockwise rotation around origin through an angle α
C
Reflection in the line through origin with slope tanα
D
Reflection in the line through origin with slope tanα/2
Solution
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Solve::
Given, P(cosθ,sinθ)
and θ(cos(αθ),sin(αθ))

slope of (PQ);m=sin(αθ)sinθcos(αθ)cosθ

=2sin(α2θ)cosα22sin(α2θ)sinα2

=cotα2

slope of line or which is perpendicular

to PQ about which we take reflection

m2=tanα2

so, reflection of P in the passing through

origin with slope tanα2

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