The tangent identity expresses the tangent of an angle in terms of the cosine and sine of the angle. To see why this is true for all angles represented by (theta) we can draw a point on a circle and write down the circle definitions of the trigonometric functions.
The key insight is that the -coordinate of the point can be written as and the -coordinate can be written as . Substituting these expressions into the definition of the tangent function we get the tangent identity.
The rest of the trigonometric identities are listed on this page.