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

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

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

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved