Duplication formulae

Setting $\beta=\alpha$ in the addition formulae gives the duplication formulae, which express the sine, cosine and tangent of the double angle $2\alpha$. The cosine has three equivalent forms: the one in sines only and the one in cosines only allow us to lower the degree of $\sin^2$ and $\cos^2$, giving rise to the extremely useful linearisation formulae.

• The duplication formulae
• Lowering the degree: linearisation formulae
• Example: linearising sin⁴α