Double Angle

Double Angle

Welcome visitors..
The trigonometric formula for double angles is derived from the trigonometric formula for the sum of angles. We take $A=B$ so that $A+B=2A=2B$. The following are trigonometric formulas for the Double Angle:

$\text{sin}(2A)=\text{sin}A.\text{cos}A+\text{sin}A.\text{cos}A$
$\text{sin}(2A)=2.\text{sin}A.\text{cos}A$

$\text{cos}(2A)=\text{cos}A.\text{cos}A-\text{sin}A.\text{sin}A$
$\displaystyle \text{cos}(2A)=\text{cos}^2A-\text{sin}^2A$

$\displaystyle \text{tan}2A=\frac{2.\text{tan}A}{1-\text{tan}^2A}$

Example:
It is known that $\text{sin }M= \frac{3}{5}$. Determine the value of $\text{sin}2M$.
Solution:
First we have to find the value of cos$M$. $$\text{cos}M=\sqrt{1-\text{sin}^2M}$$ $$=\sqrt{1-\frac{9}{25}}=\frac{4}{5}$$ So $$\text{sin}2M=2.\frac{3}{5}.\frac{4}{5}=\frac{24}{25}$$
Thanks for view, see you and happy learning.

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