Double angle identities

In trigonometry, there are four popular double angle trigonometric identities and they are used as formulae in theorems and in solving the problems. So, let’s learn each double angle identity with mathematical proof.

Sin Double angle identity

The sine of double angle is equal to two times the product of sine and cosine of angle.

$(1).\,\,$ $\sin{2\theta} \,=\, 2\sin{\theta}\cos{\theta}$

$(2).\,\,$ $\sin{2x} \,=\, 2\sin{x}\cos{x}$

Cos Double angle identity

The cosine of double angle is equal to the subtraction of square of sine from square of cosine of angle.

$(1).\,\,$ $\cos{2\theta} \,=\, \cos^2{\theta}-\sin^2{\theta}$

$(2).\,\,$ $\cos{2x} \,=\, \cos^2{x}-\sin^2{x}$

Tan Double angle identity

$(1).\,\,$ $\tan{2\theta} \,=\, \dfrac{2\tan{\theta}}{1-\tan^2{\theta}}$

$(2).\,\,$ $\tan{2x} \,=\, \dfrac{2\tan{x}}{1-\tan^2{x}}$

Cot Double angle identity

$(1).\,\,$ $\cot{2\theta} \,=\, \dfrac{\cot^2{\theta}-1}{2\cot{\theta}}$

$(2).\,\,$ $\cot{2x} \,=\, \dfrac{\cot^2{x}-1}{2\cot{x}}$

Worksheet

Learn how to use the double angle trigonometric identities as formulae in mathematical problems.