# Identity

How do you derive cos^2(x) plus sin^2(x)=1?

 dmatos Posts: 204, Reputation: 129 Full Member #2 Mar 26, 2006, 07:00 PM
Think of how the trigonometric functions are defined for a right-angled triangle.

Sin(theta) = opposite/hypotenuse.

Sin^2 + cos^2 = o^2/h^2 + a^2/h^2
= (o^2 + a^2)/h^2

But, from the pythagorean theorem,

O^2 + a^2 = h^2

Therefore,

Cos^2 + sin^2 = (o^2 + a^2)/h^2 = 1

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