Use power reduction formula to rewrite the equation in terms of cosine: cos^2x sin^4 x

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Mathematics

Alondra Cooley

19 July, 20:00

Use power reduction formula to rewrite the equation in terms of cosine: cos^2x sin^4 x

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Shelby Riley · Answer 1

Cos^2 (x) sin^4 (x) = 1/2 (1 + cos (2x)) * (1/2 (1 - cos (2x)) ^2 = 1/2 (1 + cos (2x)) * 1/4 (1 - 2cos (2x) + cos^2 (2x)) = 1/8 (1 + cos (2x)) (1 - 2cos (2x) + 1/2 + 1/2cos (4x)) = 1/16 (1 + cos (2x)) (3 - 2cos (2x) + cos (4x)) = 1/16 (3 - 2cos (2x) + cos (4x) + 3cos (2x) - 2cos^2 (2x) + cos (2x) cos (4x)) = 1/16 (3 + cos (2x) + cos (4x) - (1 + cos (4x)) + 1/2cos (6x) + 1/2cos (2x)) = 1/32 (4 + 3cos (2x) + cos (6x))