USe the trigonometric identites that we went over in class to write the following trigonometric...

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Answered question

2021-08-13

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

Answer & Explanation

grbavit

Skilled2021-08-14Added 109 answers

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