If , where ,…

MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

x\cos\alpha+y\sin\alpha=x\cos\beta+y\sin\beta=2a

, where

0<\alpha,\beta<\dfrac{\pi}{2}

, then (1)

\cos\alpha+\cos\beta=\dfrac{4ax}{x^2+y^2}

(2)

\cos\alpha\cos\beta=\dfrac{4a^2-y^2}{x^2+y^2}

(3)

\sin\alpha+\sin\beta=\dfrac{4ay}{x^2+y^2}

(4)

\sin\alpha\sin\beta=\dfrac{4a^2-x^2}{x^2+y^2}