Question

sin(x+y)sin(x-y)=sin²x-sin²y=cos²y-cos²x​

Answer 1

Answer:

first of all use the sum identity then change the sin into cos and cos into sin as you can see

similarly you can prove for

Answer 2

Given : $\sin (x+y)\sin (x-y)= \cos^2y - \cos^2x$

Step-by-step explanation:

$\sin (x+y)\sin (x-y)= \cos^2y - \cos^2x\\\\\text{solving LHS}\\\\\sin (x+y)\sin (x-y)\\\\(\sin x \cos y+\cos x \sin y)(\sin x \cos y-\cos x \sin y)\\\\(a+b)(a-b) = a^2-b^2\\\\\sin^2 x+ \cos^2y-\cos^2x\sin^2y\\\\(1-\cos^2x)\cos^2y- \cos^2x(1-\cos^2y)\\\\\cos^2y-\cos^2ycos^2x-cos^2x+cos^2xcos^2y\\\\\cos^2y-\cos^2x$

hence proved

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