Question #b2df1

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Answer 1 · 2017-10-18T16:29:30

Proved.

We have to prove, #(sin A + cos A)^2 (sin A - cos A)^2 = 1 - sin^2 (2A)#

R.H.S.

#rArr (sin A + cos A)^2 (sin A - cos A)^2#

#rArr ( sin^2 A + 2 sin A cos A + cos^2 A)(sin^2 A - 2 sin A cos A + cos^2 A)#

#rArr ( 1 + 2 sin A cos A)(1 - 2 sin A cos A)# [As,#sin^2 A+cos^2 A=1 #]

#rArr (1 + sin 2A)(1 - sin 2a)# [As, 2 sin A cos A = sin 2A]

#rArr 1 - sin^2 2A# [ As formula, #(a + b )( a - b) = a^2 - b^2#]

#rArr R.H.S.#