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

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dk_ch Share
Dec 14, 2016

Given
#sina+sin^2a=1#

#=>sina=1-sin^2a#

#=>sina=cos^2a#

#=>sin^2a=cos^4a#

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

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

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Noah G Share
Dec 14, 2016

Answer:

#1#

Explanation:

Our starting goal is to turn all terms into cosine. Use the identity #sin^2theta + cos^2theta = 1#.

#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 #sin^2theta + cos^2theta =1#:

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

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

Hopefully this helps!

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