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## Pythagorean Identities

Trigonometric identities bring new life to the Pythagorean theorem by re-envisioning the legs of a right triangle as sine and cosine. See more

# Warmup

Given $$\sin^2(\theta) + \cos^2(\theta) = 1$$, which of the following is true?

True or False: $$\sin^2(\theta) - \cos^2(\theta) + 1 = 2\sin^2(\theta)$$.

(Hint: Use the identity $$\sin^2(\theta) + \cos^2(\theta) = 1$$.)

Which is these is equivalent to $$\cos^2(\theta)\sec^2(\theta) - \cos^2(\theta),$$ over values of $$\theta$$ for which the given expression is defined?

Which of these is equivalent to $$x$$?

If $$\sin^2(\theta) = \frac{9}{25}$$, what is $$\cos^2(\theta) ?$$

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