# Prove that <msqrt> 3 </msqrt> cos &#x2061;<!-- ⁡ --> ( x ) + sin

Anthony Kramer 2022-05-24 Answered
Prove that $\sqrt{3}\mathrm{cos}\left(x\right)+\mathrm{sin}\left(x\right)=2\mathrm{cos}\left(x-\frac{\pi }{6}\right)$
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## Answers (1)

Michaela Alvarado
Answered 2022-05-25 Author has 11 answers
In the right side you can use:
$\mathrm{cos}\left(\alpha -\beta \right)=\mathrm{cos}\alpha \mathrm{cos}\beta +\mathrm{sin}\alpha \mathrm{sin}\beta \phantom{\rule{0ex}{0ex}}$
In this case:
$\mathrm{cos}\left(x-\frac{\pi }{6}\right)=\mathrm{cos}x\mathrm{cos}\frac{\pi }{6}+\mathrm{sin}x\mathrm{sin}\frac{\pi }{6}\phantom{\rule{0ex}{0ex}}\mathrm{cos}\left(x-\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}\mathrm{cos}x+\frac{1}{2}\mathrm{sin}x$
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