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

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Answer 1 · 2016-12-14T16:56:17

$1$

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!

Answer 2 · 2016-12-14T17:00:05

Given
$sina+sin^2a=1$

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

$=>sina=cos^2a$

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

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

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

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