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Solve: sin5x.cos3x = sin6x.cos2x

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Solve: sin5x.cos3x = sin6x.cos2x

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∵ sin5x.cos3x = sin6x.cos2x 

⇒ 2sin5x.cos3x = 2sin6x.cos2x 

⇒ sin8x + sin2x = sin8x + sin4x 

⇒ sin4x – sin2x = 0 ⇒ 2sin2x.cos2x – sin2x = 0 

⇒ sin2x (2cos2x – 1) = 0 

⇒ sin2x = 0 or 2cos2x – 1 = 0

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