Sin2 6x - sin2 4x = sin 2x sin10x

1.	Sin2 6x - sin2 4x = sin 2x sin10x
Answer» Hi<br>LHS = sin²(6x) - sin²(4x)Use the formula,(a² - b²) = (a - b)(a + b)= (sin6x -sin4x)(sin6x +sin4x)Now,Use the formula,sinC + sinD = 2sin(C+D)/2.cos(C-D)/2sinC - sinD = 2cos(C+D)/2.sin(C-D)/2={2cos(6x+4x)/2.sin(6x-4x)/2}{2sin(6x+4x)/2.cos(6x-4x)/2}={2cos5x.sinx}{2sin5x.cosx}={2sin5x.cos5x}{2sinx.cosx}Use the formula,sin2A = 2sinA.cosA= sin2(5x).sin2(x)= sin10x.sin2x =RHS

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