SOLUTION: establish each identity sin^2 theta cos^2 theta = 1/8[ 1- cos(4 theta)]

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Question 703828: establish each identity
sin^2 theta cos^2 theta = 1/8[ 1- cos(4 theta)]
Answer by nshah11(47) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that sin(2θ) = 2sin(θ)cos(θ) => sin(2θ)/2 = sin(θ)cos(θ)
sin^2(θ) * cos^2(θ) = (sin(2θ)/2)^2 = 1/4*sin^2(2θ)
Simplifying that further and remembering that sin^2(θ) = (1 - cos(2θ))/2
1/4*sin^2(2θ) = 1/8 * (1 - cos(4θ))