butterfly987
Answered

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If cosƟ+cos2Ɵ =1,the value of sin2Ɵ+sin4Ɵ is

(a) -1
(b) 0
(c) 1
(d) 2

Sagot :

brundag05

It came rude when I typed. so, I took screenshot for your answer.

PLEASE MARK ME BRAINLIEST

View image brundag05
MrRoyal

The given equation are illustrations of trigonometry identities. The value of [tex]\sin^2\theta + \sin^4\theta[/tex] is 1

Given that:

[tex]\cos \theta + \cos^2 \theta = 1[/tex]

In trigonometry:

[tex]\sin^2 \theta + \cos^2\theta = 1[/tex]

Rewrite as:

[tex]\sin^2 \theta = 1 - \cos^2\theta[/tex]

Make [tex]\cos \theta[/tex] the subject in [tex]\cos \theta + \cos^2 \theta = 1[/tex]

[tex]\cos\theta = 1 - \cos^2 \theta[/tex]

Compare [tex]\sin^2 \theta = 1 - \cos^2\theta[/tex] and [tex]\cos\theta = 1 - \cos^2 \theta[/tex]

[tex]\sin^2 \theta = \cos \theta[/tex]

So:

[tex]\sin^2\theta + \sin^4\theta[/tex] becomes

[tex]\sin^2\theta + \sin^4\theta = \sin^2\theta + (\sin^2\theta)^2[/tex]

Substitute [tex]\sin^2 \theta = \cos \theta[/tex]

[tex]\sin^2\theta + \sin^4\theta = cos\theta + (cos\theta)^2[/tex]

[tex]\sin^2\theta + \sin^4\theta = cos\theta + cos^2\theta[/tex]

Recall that: [tex]\cos \theta + \cos^2 \theta = 1[/tex]

This means:

[tex]\sin^2\theta + \sin^4\theta = 1[/tex]

Hence, the value of [tex]\sin^2\theta + \sin^4\theta[/tex] is 1

Read more about trigonometry identities at:

https://brainly.com/question/63577

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