Step by step solution to "Solve (sin⁡θ+cos⁡θ)cos⁡θ+(sin⁡θ−cos⁡θ)cos⁡θ"

Joni Kenny

Answered question

2021-03-04

Solve

\frac{(\sin θ + \cos θ)}{\cos θ} + \frac{(\sin θ - \cos θ)}{\cos θ}

Layton

Skilled2021-03-05Added 89 answers

\frac{\sin (θ) + \cos (θ)}{\cos (θ)} + \frac{\sin (θ) - \cos (θ)}{\cos (θ)} =

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= (\sin (θ) + \cos (θ) + \sin (θ) - \frac{\cos (θ)}{\cos (θ)}

= \frac{2 \sin (θ)}{\cos (θ)}

Use the following identity:

\sin (x) \cos (x) = \tan (x)

= 2 \tan (θ)

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