# 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 2*A*. We often call the identities used to find the function values of twice an angle **double-angle formulas**.

**Sine of 2 A**

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

Also Read:

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

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

**sin (2 A) **=

**2 sin**

*A*cos*A***Cosine of 2 A**

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 (2 A) **=

**cos**–

^{2}*A***sin**

^{2}*A*The identity for cos 2*A *can be written in two other ways:

cos (2A) = 2 cos^{2} – 1

cos (2A) = 1 – 2sin^{2} A

**Also Read : **How to determine of tangent (A – B) and tangent (A + B)

**Tangent of 2 A**

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