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Question

sin(a-b) sin(a+b) = sin^2 a - sin^2 b

Answer 1

sin(a-b) = sina cosb - cosa sinb
sin(a+b) = sina cosb + cosa sinb

since (u-v)(u+v) = u^2-v^2, we have

(sina cosb)^2 - (cosa sinb)^2
sin^2 a cos^2 b - cos^2 a sin^2 b
sin^2 a (1 - sin^2 b) - (1 - sin^2 a) sin^2 b
sin^2 a - sin^2 b