Question

2. If sin 0 + sin2 0 =1, prove that cos2 0 + cos4 0 =1.​

Answer 1

Given:

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

To prove that: $\cos^2 \theta$ + $\cos^4 \theta$ = 1.

Solution:

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

⇒ $\sin \theta$ = 1 - $\sin^2 \theta$

Using the trigonometric identity,

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

⇒ $\sin \theta$ = $\cos^2 \theta$

Squaring both sides, we get

$\sin^2 \theta$ = $(\cos^2 \theta)^2$

⇒ $\sin^2 \theta$ = $\cos^4 \theta$

⇒ 1 - $\cos^2 \theta$  = $\cos^4 \theta$

Using the trigonometric identity,

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

⇒ $\cos^2 \theta$ + $\cos^4 \theta$ = 1, proved.

Thus, if $\sin \theta$ + $\sin^2 \theta$ = 1, then $\cos^2 \theta$ + $\cos^4 \theta$ = 1, proved.

Answer 2

Step-by-step explanation:

your ans is 1....

hope you are satisfied with the attached answer