Question

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

Answer 1

`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!

Answer 2

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`