# Double angle formulas

### Sine Double angle formulas

Sine of double angle can be expanded in two different forms.

$(1)\,\,\,\,$ $\sin 2 \theta \,=\, 2\sin \theta \cos \theta$

$(2)\,\,\,\,$ $\sin 2 \theta \,=\, \dfrac{2 \tan \theta}{1+\tan^2 \theta}$

### Cosine Double angle formulas

Cosine of double angle can be expanded in three different forms.

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

$(2)\,\,\,\,$ $\cos 2 \theta = 2\cos^2 \theta -1$

$(3)\,\,\,\,$ $\cos 2 \theta = 1 -2\sin^2 \theta$

### Tangent Double angle formulas

Tangent of double angle can be expanded in two different forms.

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

$(2)\,\,\,\,$ $\tan 2 \theta = \dfrac{2}{\cot \theta -\tan \theta}$

### Cotangent Double angle formulas

Cotangent of double angle can be expanded in two different forms.

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

$(2)\,\,\,\,$ $\cot 2 \theta = \dfrac{\cot \theta -\tan \theta}{2}$