Triple angle identities

Sin triple angle identity

$(1).\,\,$ $\sin{3\theta}$ $\,=\,$ $3\sin{\theta}-4\sin^3{\theta}$

$(2).\,\,$ $\sin{3x}$ $\,=\,$ $3\sin{x}-4\sin^3{x}$

Cos triple angle identity

$(1).\,\,$ $\cos{3\theta}$ $\,=\,$ $4\cos^3{\theta}-3\cos{\theta}$

$(2).\,\,$ $\cos{3x}$ $\,=\,$ $4\cos^3{x}-3\cos{x}$

Tan triple angle identity

$(1).\,\,$ $\tan{3\theta}$ $\,=\,$ $\dfrac{3\tan{\theta}-\tan^3{\theta}}{1-3\tan^2{\theta}}$

$(2).\,\,$ $\tan{3x}$ $\,=\,$ $\dfrac{3\tan{x}-\tan^3{x}}{1-3\tan^2{x}}$

Cot triple angle identity

$(1).\,\,$ $\cot{3\theta}$ $\,=\,$ $\dfrac{3\cot{\theta}-\cot^3{\theta}}{1-3\cot^2{\theta}}$

$(2).\,\,$ $\cot{3x}$ $\,=\,$ $\dfrac{3\cot{x}-\cot^3{x}}{1-3\cot^2{x}}$

Problems

The list of trigonometry questions with understandable solutions on triple angle identities to learn how to use them as formulas in problems.