Question

if sin thita+ sin2thita = 1 prove that cos2thita + cos4thita = 1​

Answer 1

Explanation:

Our starting goal is to turn all terms into cosine. Use the identity ---> sin2θ+cos2θ=1

sina+1−cos2a=1

sina−cos2a=0

sina=cos2a

Square both sides to get rid of the sine.

(sina)2=(cos2a)2

sin2a=cos4a

Reuse sin2θ+cos2θ=1 :

1−cos2a=cos4a

1=cos4a+cos2a

Hopefully this helps!

Answer 2

Since

$\sin(a) + {sin}^{2} a = 1$

$sin(a) = {sin}^{2} a + {cos}^{2} a - {sin}^{2} a$

$sin(a) = {cos}^{2} a$

If we substitute this value in

$sin(a) + {sin}^{2} a = 1$

We get

${cos}^{2} a + {cos}^{4} a = 1$

Hence proved