In right angle triangles there is one 90 degree angle and two other angles that are said to be complementary angles on the basis that the sum of interior angles of a triangle is 180 degrees.

Since the two angles A and B are complementary angles they have special properties that allow us to manipulate certain trigonometric identities for right angle triangles. I originally noticed this while I was looking at compound angle formulas and realized that if the angles are complementary then it results in the co-function identities. I then appplied this theory to the Pythagorean identities and proved a new identity for right angle triangles.

The pythagorean identity states that:

sin^2(A)+cos^2(A)=1

sin^2(B)+cos^2(B)=1

In a right angle triangle this translates to:

sin^2(A)+sin^2(B)=1

cos^2(A)+cos^2(B)=1

## Comments

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TopNewestAre you sure that \( \sin ^2 A + \cos^2 B = 1 \)? Why?

Shouldn't it be \( \sin^2 \theta + \cos^2 \theta = 1 \)? – Calvin Lin Staff · 2 years ago

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– Brody Acquilano · 2 years ago

oops yes i will have to edit that, thanks!Log in to reply