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Mathematics

Trigonometric Identities and How to Derive Them

Quick fact

The angle addition formula for sine, sin(A+B) = sin A cos B + cos A sin B, is not just a rule—it can be derived from the unit circle by comparing the coordinates of rotated points.

Why this is interesting

You know that sin²θ + cos²θ = 1, but have you ever wondered why it's true for every angle? And where do the double-angle formulas come from? The answers lie in a simple circle.