Question

If sinø+sin2ø=1,then cos2 ø+cos4 ø=?

Answer 1

Answer:

1

Explanation:

Given,

$\sf sin\theta +\sin^2\theta=1\\\\\implies sin\theta + sin^2\theta = sin^2\theta + cos^2\theta \\\\(since, sin^2\theta + cos^2\theta = 1) \\\\\implies sin\theta = cos^2\theta......(1) \\\\(cancelling\ sin^2\theta\ from\ both\ sides) \\\\Now, on \ squaring \ both \ sides, we\ get \\\\\implies cos^4\theta = sin^2\theta ........(2) \\\\Now, add \ (1)\ and\ (2) \\\\\implies cos^2\theta + cos^4\theta = sin\theta + sin^2\theta \\\\\implies cos^2\theta + cos^4\theta = 1$

$\sf (since, given\ sin^2\theta + sin\theta = 1)$

Hence, the answer is 1

Answer 2

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