Trigonometric Equations - Double Angle Formula
The trigonometric double angle formulas give a relationship between the basic trigonometric functions applied to twice an angle in terms of trigonometric functions of the angle itself.
Double Angle Formulas
Double angle formulas:
We have
We can prove the double angle identities using the sum formulas for sine and cosine:
From these formulas, we also have the following identities:
Hyperbolic Double Angle Formulas
We have
Examples
Prove the identity
We have
Prove the identity
We have
Prove the identity
We have
Here goes some important terminology:
- versed sine
- versed cosine
- coversed sine
- coversed cosine