Question

if sin theta + sin ^2 theta = 1 , then find the value of cos^2 theta + cos^4 theta

Answer 1

this is the answer of the math

Answer 2

$\sinθ + { \sin }^{2} θ = 1$
----(i)

You might know that,
${ \sin }^{2} θ + { \cos }^{2} θ = 1$
Using the identity in (i)

$\sinθ + { \sin }^{2} θ = { \sin }^{2} θ + { \cos }^{2} θ \\ \\ \sinθ = { \cos}^{2} θ \\ \\ \cosθ = \sqrt{ \sinθ }$
----(ii)

Substituting this value in the asked equation,


Cos^2 θ + cos^4 θ

gives,

Sinθ + sin^2 θ which is equal to 1.

Hence proved.