Double-Angle and Half-Angle Identities

Question 1

What are the Double-Angle Identities?

Answer 1

sin 2 (theta) = 2 sin theta cos theta.

cos 2 (theta) = cos^2(theta) - sin^2 theta.
cos 2 (theta) = 2 cos^2(theta) - 1.
cos 2 (theta) = 1 - 2 sin^2 (theta).

tan 2 (theta) = 2tan theta/1 - tan^2 theta.

Question 2

What are the Half-Angle Identities?

Answer 2

sin theta/2 = +/- sqrt((1 - cos theta)/2).
cos theta/2 = +/- sqrt((1 + cos theta)/2).
tangent theta/2 = +/- sqrt((1 - cos theta)/1 + cos theta).