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Drongoski · Jul 30, 2022

LHS

= $(sin(A+B) + sin(A-B)) \times (sin(A+B) - sin(A-B))\\ \\ =[(sinAcosB + cosAsinB) + (sinAcosB - cosAsinB)] \times [(sinAcosB + cosAsinB) - (sinAcosB - cosAsinB)] \\ \\ = 2sinAcosB \times 2sinBcosA \\ \\ = 2sinAcosA \times 2sinBcosB \\ \\ sin2A \times sin2B$

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