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Question 48
What is the value of $$\frac{[(\sin x + \sin y) (\sin x - \sin y)]}{[(\cos x + \cos y) (\cos y - \cos x)]}?$$
Solution
$$\dfrac{[(\sin x + \sin y) (\sin x - \sin y)]}{[(\cos x + \cos y) (\cos y - \cos x)]}$$
=$$\dfrac{sin^{2}x-sin^{2}y}{cosxcosy-cosxcosy+cos^{2}x-cos^{2}y}$$
=$$\dfrac{sin^{2}x-sin^{2}y}{1-sin^{2}x-(1-sin^{2}y)}$$
=$$\dfrac{sin^{2}x-sin^{2}y}{sin^{2}x-sin^{2}y}$$
=1
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