Show that the product of sines of the sum and difference of two angles can be written…

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Show that the product of sines of the sum and difference of two angles can be written as sin⁡(x+y) sin⁡(x−y)=sin⁡2x−sin⁡2y.\sin(x+y)\,\sin(x-y)=\sin^{2}x-\sin^{2}y. Provide a complete algebraic proof valid for all real xx and yy.

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