Question

If sin theta + sin2 theta = 1 Then prove that cos2 theta + sin4 theta = 1

Answer 1

$cos^4\theta + cos^2\theta = 1$ is proved

Step-by-step explanation:

Given:

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

To Prove:

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

We know that,

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

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

$\\\cos^2\theta = 1-sin^2\theta$..........(3)

Now substituting equation (3) in (1) we get,

$sin\theta = cos^2\theta$

Squaring on both sides we get

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

$sin^2\theta = cos^4\theta$................(4)

Substituting equation (2) in (4) we get,

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

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

Hence Proved.

The correct question is if sin theta +sin^2 theta = 1, then prove that cos^2 theta + cos^4 theta = 1

To Learn More.....

1.Show that (cosec theta-cot theta) 2 =1-cos theta/ 1+cos theta

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2.Prove that (cosec theta+sin theta)(cosec theta-sin theta)=cot square theta+cos square theta

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