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## Answered question

2021-08-11

Find the value of expression
$\mathrm{cos}\left(pt+\alpha \right)\mathrm{cos}\left(pt+\beta \right)$

### Answer & Explanation

BleabyinfibiaG

Skilled2021-08-12Added 118 answers

Given:
$\mathrm{cos}\left(pt+\alpha \right)\mathrm{cos}\left(pt+\beta \right)$
We know that
We know that $2\mathrm{cos}A\mathrm{cos}B=\mathrm{cos}\left(A+B\right)+\mathrm{cos}\left(A-B\right)$
Apply this Result on Equation
$\mathrm{cos}\left(pt+\alpha \right)+\mathrm{cos}\left(pt+\beta \right)=\frac{1}{2}\left(\mathrm{cos}\left(2pt+\alpha +\beta \right)+\mathrm{cos}\left(\alpha -\beta \right)$
$=\frac{1}{2}\left[\mathrm{cos}\left(2pt+\alpha +\beta \right)+\mathrm{cos}\left(\alpha -\beta \right)\right]$
$=\frac{\mathrm{cos}\left(2p+\alpha +\beta \right)}{2}+\frac{\mathrm{cos}\left(\alpha -\beta \right)}{2}$

Jeffrey Jordon

Expert2021-12-12Added 2605 answers

Answer is given below (on video)

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