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A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.

cos^4θ - sin^4θ + sin^2θ

(cos^2θ + sin^2θ)(cos^2θ - sin^2θ) + sin^2θ Pythagorean identity: (cos^2θ + sin^2θ) = 1

(cos^2θ - sin^2θ) + sin^2θ = cos^2θ <-- ANSWER