How do you use the double angle or half angle formulas to derive cos(4x) in terms of cos x? Trigonometry Trigonometric Identities and Equations Double Angle Identities 2 Answers - [Voiceover] All right, let's see if we can find the limit of 1 over the square root of 2 sine of theta over cosine of 2 theta, as theta approaches negative pi over 4. And like always, try to give it a shot before we go through it together. Well, one take on it is well, let's just, let's just say ... The Double-Angle formulas express the cosine and sine of twice an angle in terms of the cosine and sine of the original angle. We are going to derive them from the addition formulas for sine and cosine. Sine or Cosine of a Double Angle. With equation 48, you can find sin(A + B). What happens if you set B = A? sin(A + A) = sin A cos A + cos A sin A. But A + A is just 2A, and the two terms on the right-hand side are equal. Therefore: sin 2A = 2 sin A cos A. The cosine formula is just as easy: cos(A + A) = cos A cos A − sin A sin A. cos 2A = cos² A − sin² A Double angle formulas are allowing the expression of trigonometric functions of angles equal to 2u in terms of u, the double angle formulas can simplify the functions and gives ease to perform more complex calculations. The double angle formulas are useful for finding the values of unknown trigonometric functions.