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Prove that the image of point P(costheta, sin theta) in the line having slope tan(alpha//2) and passing through origin is Q(cos(alpha-theta),sin(alpha-theta)). |
Answer» SOLUTION :  Clearly, `OP=OQ=1` Now, we have to prove that Q is the image of P in the LINE OR which has slope tan `(alpha//2)`. Triangle `POQ` is isosceles triangle. If Q is the image of P in line OR, then OR is the PERPENDICULAR bisector of PQ. We have to prove that `angle QOM=alpha-THETA`. `angle ROQ=angle POR=theta-(alpha//2)` `THEREFORE angle QOM=angleROM-angle ROQ` `=(alpha//2)-(theta-(alpha))=alpha-theta` |
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