# The function of double – angle (2A) of trigonometric

The identities for sin (A + B), cos (A + B), and tan (A + B) are true when A = B. These identities can be used to find the function values of 2A. We often call the identities used to find the function values of twice an angle double-angle formulas.

Sine of 2A

In the identity for sin (A + B), let B = A.

sin (A + B) = sin A cos B + cos A sin B

sin (A + A) = sin A cos A + cos A sin A

sin (2A) = 2 sin A cos A

Cosine of 2A

In the identity for cos (A + B), let B = A.

cos (A + B) = cos A cos B = sin A sin B

cos (A + A) = cos A cos A – sin A sin A

cos (2A) = cos2 A sin2 A

The identity for cos 2A can be written in two other ways:

cos (2A) = 2 cos2 – 1

cos (2A) = 1 – 2sin2 A

Tangent of 2A

In the identity for tan (A + B), let B = A.

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

$\tan (A+A)=\frac{\tan A+\tan A}{1-\tan A\tan A}$

$\tan 2A=\frac{2\tan A}{1-\tan^2A}$