Joni Kenny

Answered question

2021-03-04

Solve $\frac{\left(\mathrm{sin}\theta +\mathrm{cos}\theta \right)}{\mathrm{cos}\theta }+\frac{\left(\mathrm{sin}\theta -\mathrm{cos}\theta \right)}{\mathrm{cos}\theta }$

Answer & Explanation

Layton

Skilled2021-03-05Added 89 answers

$\frac{\mathrm{sin}\left(\theta \right)+\mathrm{cos}\left(\theta \right)}{\mathrm{cos}\left(\theta \right)}+\frac{\mathrm{sin}\left(\theta \right)-\mathrm{cos}\left(\theta \right)}{\mathrm{cos}\left(\theta \right)}=$
Apply rule $\frac{a}{c}±\frac{b}{c}=\frac{a±b}{c}$
$=\left(\mathrm{sin}\left(\theta \right)+\mathrm{cos}\left(\theta \right)+\mathrm{sin}\left(\theta \right)-\frac{\mathrm{cos}\left(\theta \right)}{\mathrm{cos}\left(\theta \right)}$
$=\frac{2\mathrm{sin}\left(\theta \right)}{\mathrm{cos}\left(\theta \right)}$
Use the following identity: $\mathrm{sin}\left(x\right)\mathrm{cos}\left(x\right)=\mathrm{tan}\left(x\right)$
$=2\mathrm{tan}\left(\theta \right)$

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