$\cos{3\theta} \,=\, 4\cos^3{\theta}-3\cos{\theta}$

$4\cos^3{\theta}-3\cos{\theta} \,=\, \cos{3\theta}$

It is called cos triple angle identity and used as a formula in two various cases.

- Cos of triple angle is expanded as the subtraction of three times cos of angle from four times cos cubed of angle.
- The subtraction of three times cos of angle from four times cos cubed of angle is simplified as cos of triple angle.

Cosine of triple angle identity is used to either expand or simplify the triple angle cos functions like $\cos{3x}$, $\cos{3A}$, $\cos{3\alpha}$ and etc. For example,

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

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

$(3) \,\,\,\,\,\,$ $\cos{3\alpha} \,=\, 4\cos^3{\alpha}-3\cos{\alpha}$

Learn how to derive the rule of cos triple angle identity by geometric approach in trigonometry.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.