Question

sinQ + sin2Q=1.Then cos2Q + cos4Q=

Answer 1

The value of $\cos^{2} \theta + \cos^{4} \theta$ = 1

Step-by-step explanation:

Given that

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

$\sin \theta = 1 - \sin^{2}\theta$

we know that $1 - \sin^{2} \theta = \cos ^{2}\theta$

$\sin\theta = \cos^{2} \theta$ ------- (1)

Thus $\cos^{2} \theta + \cos^{4} \theta$ may be written as

$\cos^{2} \theta + (\cos^{2} \theta}) ^{2}$ ------ (2)

Put the value of $cos^{2} \theta$ in above equation. the above equation becomes,

$\sin\theta + sin^{2} \theta$ ------ (3)

We know that $\sin\theta + sin^{2} \theta$ = 1  thus

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

Thus the value of $\cos^{2} \theta + \cos^{4} \theta$ = 1