Solving Pythagorean Identities
The Pythagorean identities in trigonometry are the three identities that come from the Pythagorean theorem.
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Recall that the Pythagorean theorem states that the hypotenuse squared of a right triangle is the sum of the square of each of the other two sides.
a2 + b2 = c2
Where c stands for the hypotenuse, and a and b are other two sides of the right triangle.
From this theorem, three identities can be determined from substituting in sine and cosine as follows:
sin2 θ + cos2 θ = 1
tan2 θ + 1 = sec2 θ
1 + cot2 θ = cosec2 θ