DoubleAngle and Half‐Angle Identities. Because sin x is positive, angle x must be in the first or second quadrant. The sign of cos 2 x will depend on the size of angle x. A doubleangle function is written, for example, as sin 2θ, cos 2α, or tan 2x, where 2θ, 2α, and 2x are the angle measures and the assumption is that you mean sin(2θ), cos(2α), or tan(2x). Because tangent is equal to the ratio of sine and cosine, its identity comes from their double-angle identities.

Double angle Identity

Double angle identity