Question

Prove that :
(sin 5 A / Sin A) - ( cos 5 A / cos A) = 4 cos 2 A​

Answer 1

Answer:

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Answer 2

L.H.S:-

(sin 5A/sin A) - (cos 5A/cos A)

= (sin 5A.cos A-cos 5A.sin A)/(sinA.cosA)

= sin(5A - A)/(sin A.cos A)

= sin 4A/(sin A.cos A)

= 2 sin 4A/(2×sin A. cos A)

= 2× (2 sin 2A.cos 2A)/(sin 2A)

= 4 cos 2A = R.H.S

Hence, L.H.S = R.H.S (proved) .

Hope it helps to you .