Use the squared identities to simplify 2sin^2xsin^2x

[3-4 cos (2 x) + cos (4 x) ]/4

Step-by-step explanation:

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2sin^2 (x) sin^2 (x) = 2sin^4 (x);

cos (4x) = 2cos^2 (2x) - 1 ... (1)

cos (2x) = 1 - 2sin^2 (x) ... (2)

Substituting cos2x from (2) in (1).

We get cos (4x) = 1 + 8sin^4 (x) - 8sin^2 (x);

Thus we get 2sin^4 (x) = (cos (4x) - 1) / 4 + 2sin^2 (x);

Substituting sin^2 (x) from (2):

2sin^4 (x) = [3-4cos (2x) + cos (4x) ]/4