How to prove sin^2 (A)*cos^2 (A) = 1/8 (1-cos (4A)) ?

1 Answer
Ratnaker Mehta
Sep 24, 2017

Please refer to the Explanation.

Explanation:

We use, # sin^2B=1/2(1-cos2B), &, cos^2B=1/2(1+cos2B).#

#:. sin^2A*cos^2A={1/2(1-cos2A)}{1/2(1+cos2A)},#

#=1/4(1-cos^2 2A),#

#=1/4{1-1/2(1+cos4A)},#

#=1/4(1/2-1/2*cos4A),#

#=1/8(1-cos4A).#

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