Double angle formulas

1

Sine of double angle formula

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

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

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

Learn proof of sin of double angle in terms of sin and cos of angle and also learn the proof of the expansion of sin of double angle in terms of tan of angle.

2

Cosine of double angle formula

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

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

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

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

3

Tangent of double angle formula

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

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

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

4

Cotangent of double angle formula

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

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

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

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