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Use the power reducing formulas to rewrite cos^4x in terms of the first power of cosine.
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Use the power reducing formulas to rewrite cos^4x in terms of the first power of cosine.
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We need to know that
cos²(x) = 0.5 + 0.5 cos(2x)
Solution:
cos⁴(x) = (cos²(x))² = (0.5 + 0.5 cos(2x))² = 0.25 + 0.5 cos(2x) + 0.25 cos²(2x) =
= 0.25 + 0.5 cos(2x) + 0.25 (0.5 + 0.5 cos(4x)) = 0.25 + 0.5 cos(2x) + 0.125 + 0.125 cos(4x) =
= 0.375 + 0.5 cos(2x) + 0.125 cos(4x)
or
cos⁴(x) = 3/8 + (1/2) cos(2x) + (1/8) cos(4x)