# If #sina + sin^2a = 1,# then what will be# cos^2a + cos^4a #?

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dk_ch
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Dec 14, 2016

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Then teach the underlying concepts

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Noah G
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Dec 14, 2016

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Our starting goal is to turn all terms into cosine. Use the identity

#sina + 1 - cos^2a = 1#

#sina - cos^2a = 0#

#sina = cos^2a#

Square both sides to get rid of the sine.

#(sina)^2 = (cos^2a)^2#

#sin^2a = cos^4a#

Reuse

#1 - cos^2a = cos^4a#

#1 = cos^4a + cos^2a#

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