Question

Sin5A/SinA-cos5A/cosA=4cos2A​

Answer 1

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Explanation:

`( \sin5A)/(\sin A) - ( \cos5A)/(\cos A) = 4\cos2A \\ \\ LHS = ( \sin5A)/(\sin A) - ( \cos5A)/(\cos A) \\ \\ = ( \sin5A \:\cos A - \cos5A \: \sin A)/(\sin A \:\cos A ) \\ \\ = ( \sin(5A -A ))/(\sin A \:\cos A) \\ \\ = ( \sin 4A)/(\sin A \:\cos A) \\ \\ = ( 2\sin 2A \: \cos 2A)/(\sin A \:\cos A) \\ \\ = ( 2 * 2\sin A \: \cos A \: \cos 2A)/(\sin A \:\cos A) \\ \\ = ( 4\sin A \: \cos A \: \cos 2A)/(\sin A \:\cos A) \\ \\ =4\cos 2A \\ \\ = RHS \\ \\ thus \\ \\ ( \sin5A)/(\sin A) - ( \cos5A)/(\cos A) = 4\cos2A \\ \\ hence \: proved`