Number One Identity

$Sin\theta=1-sin^2\theta$

$Sin\theta = cos^2\theta$

So

$cos^4\theta$ = $sin^2\theta$

$cos^2\theta +cos^4\theta = sin\theta + sin^2\theta = 1$

---

Upvote if you are satisfied

Given

$\sin \theta$ + $\sin^2 \theta$ =1 ---->(1)

Identity I $\Rightarrow$ $\sin^2 \theta$ + $\cos^2 \theta$ =1 ---->(2)

By comparing (1)=(2)

We get $\sin \theta$ = $\cos^2 \theta$

If $\sin \theta$ = $\cos^2 \theta$ , then $\sin^2 \theta$ = $\cos^4 \theta$

Therefore $\cos^2 \theta$ + $\cos^4 \theta$ = $\sin \theta$ + $\sin^2 \theta$

$\Rightarrow$ $\cos^2 \theta$ + $\cos^4 \theta$ = $\boxed{1}$

We know sin^2 theta+cos^2 theta=1 It is given, sin theta+sin^2 theta=1 so sin theta=cos^2 theta to find cos^2 theta+cos^4 theta substitute sin theta in place of cos^2 theta and sin^2 theta in place of cos^4 theta we get sin theta+sin^2 theta=? value is already given as 1 ans is 1

Ans: 1 cos²θ = 1 - sin²θ = 1 - (1 - sin θ) = sin θ cos²θ + cos⁴θ = cos²θ(1 + cos²θ) = sin θ(1 + sin θ) = sin θ + sin²θ = sin θ + (1 - sin θ) = 1