Anonym

2021-08-13

USe the trigonometric identites that we went over in class to write the following trigonometric expression in its most reduced form
${\mathrm{cos}}^{2}\left(5x\right)$

grbavit

Given expression,
${\mathrm{cos}}^{2}\left(5x\right)$
Making use of the trignometric identity
$\mathrm{cos}\left(2x\right)=2{\mathrm{cos}}^{2}x-1$
$⇒{\mathrm{cos}}^{2}x=\frac{1+\mathrm{cos}\left(2x\right)}{2}$
Now
${\mathrm{cos}}^{2}\left(5x\right)=\frac{1+\mathrm{cos}2\left(5x\right)}{2}$
$=\frac{1+\mathrm{cos}2\left(5x\right)}{2}$
$=\frac{1+\mathrm{cos}\left(10x\right)}{2}$
$=\frac{1}{2}+\frac{\mathrm{cos}\left(10x\right)}{2}$
${\mathrm{cos}}^{2}\left(5x\right)=\frac{1}{2}+\frac{\mathrm{cos}\left(10x\right)}{2}$

Jeffrey Jordon