Prove that sin²6x-sin²4x = sin2x sin10x
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Taking RHS sideSin2x sin10xSin(6x-4x) sin(6x+4x)(Sin6xcos4x – cos6xsin4x)(sin6xcos4x+cos6xsin4x) : (since-sin(A+B)=sinAcosB+sinBcosA)(sin(A+B)=sinAcosB- sinBcosA)Sin^2(6x)cos^2(4x) – cos^2(6x)sin^2(4x)Sin^2(6x)(1 – sin^2(4x)) – (1 – sin^2(6x))sin^2(4x)Sin^2(6x) – sin^2(4x)sin^2(4x) – sin^2(4x) + sin^2(6x )sin^2(4x)Sin^2(6x) – sin^2(4x) Hence . Proved
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LHS= sin(6x-4x)sin(6x+4x) =sin2xsin10x = RHS