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) Sin 10x sin 2prove that : cos2 2x-cos2 6x = sin 4x sin 8x |
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Answer» LHS =cos²(2x) - cos²(6x) Use the formula, a² - b² = (a - b)(a + b) = (cos2x - cos6x)(cos2x + cos6x)Use the formulacosC + cosD = 2cos(C+D)/2.cos(C-D)/2cosC - cosD = 2sin(C+D)/2.sin(D-C)/2 = {2sin(2x + 6x)/2.sin(6x-2x)/2}{2cos(2x+6x)/2.cos(6x -2x)/2}={2sin2x.sin4x}{2cos4x.cos2x}={2sin2x.cos2x}{2sin4x.cos4x} Now, Use the formula, sin2A = 2sinA.cosA = sin2(2x).sin2(4x)= sin4x.sin8x = RHS |
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