Prove the following: sin26x - sin24x = sin2x sin10x

LHS=sin26x−sin24x=(sin6x+sin4x)(sin6x−sin4x)... [∵a2−b2=(a+b)(a−b)]We know that,sinA+sinB=2sin(A+B2)cos(A−B2)∴LHS=[2sin(6x+4x2)cos(6x𕒸x2)][2cos(6x+4x2)sin(6x𕒸x2)]=[2sin(10x2)cos(2x2)][2cos(10x2)sin(2x2)]=2sin5xcosx×2cos5xsinx=2sin5xcos5x×2sinxcosx=sin10x×sin2x...[∵sin2θ=2sinθcosθ]=RHSHence proved.