The following identities equate
trigonometric functions of double angles to expressions that involve only
trigonometric functions of single angles. They are very useful in
differentiation and other general simplification.
|cos(2x) = cos2(x) - sin2(x) = 1 - 2 sin2(x) = 2 cos2(x) - 1||
|tan(2x) = ||
The following identities equate trigonometric functions of half-angles to
expressions that involve only trigonometric functions of single angles.
If an angle in question is a variable, these formulas are sometimes the only
means by which the trigonometric expression can be simplified. Even when an
angle is known, these identities can be useful in simplifying expressions. They
should be memorized.
One additional formula is useful in conjunction with triangles. For any
triangle ABC, tan() = where s is the semiperimeter
(s = ) and k = .
This is another way to express the half-angle formula for tangent.