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13-102.

Rewrite the Pythagorean Identity as many ways as you can. One way to change the identity would be to solve the equation for one trigonometric function. Another way is to use factoring. Try several different ways. Homework Help ✎

Recall the Pythagorean Identity.

sin2(x) + cos2(x) = 1

Subtract cos2(x) from each side.

Take the square root of both sides.

Factor the equation sin2(x) = 1 − cos2(x).

sin2(x) = 1 − cos2(x)

$\text{sin}(x)=\pm\sqrt{1-\text{cos}^2(x)}$

sin2(x) = (1 − cos(x))(1 + cos(x))

Similar variations for cosine in terms of sine are also appropriate.