In some cases, it is essential to express trigonometric functions in terms of sum multiple angle trigonometric functions to find their values mathematically. So, learn how to expand trigonometric functions in terms of trigonometric functions which contain sub multiple angles. The following submultiple angle identities are used as formulae in trigonometric mathematics but they are similar to multiple angle formulas.

Learn how to expand trigonometric functions in terms of half angle trigonometric functions.

$(1)\,\,\,\,$ $\sin{\theta}$ $\,=\,$ $2\sin{\Big(\dfrac{\theta}{2}\Big)}\cos{\Big(\dfrac{\theta}{2}\Big)}$

$(2)\,\,\,\,$ $\cos{\theta}$ $\,=\,$ $\cos^2{\Big(\dfrac{\theta}{2}\Big)}-\sin^2{\Big(\dfrac{\theta}{2}\Big)}$

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

$(4)\,\,\,\,$ $\cot{\theta}$ $\,=\,$ $\dfrac{\cot^2{\Big(\dfrac{\theta}{2}\Big)}-1}{2\cot{\Big(\dfrac{\theta}{2}\Big)}}$

Learn how to expand trigonometric functions in terms of one third angle trigonometric functions.

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

$(2)\,\,\,\,$ $\cos{\theta}$ $\,=\,$ $4\cos^3{\Big(\dfrac{\theta}{3}\Big)}-3\cos{\Big(\dfrac{\theta}{3}\Big)}$

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

$(4)\,\,\,\,$ $\cot{\theta}$ $\,=\,$ $\dfrac{3\cot{\Big(\dfrac{\theta}{3}\Big)}-\cot^3{\Big(\dfrac{\theta}{3}\Big)}}{1-3\cot^2{\Big(\dfrac{\theta}{3}\Big)}}$

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved