Step by step solution to "How to simplify sin⁡(θ+π)cos⁡(θ−π)?"

Memphis Burnett

Answered question

2023-01-20

How to simplify

\frac{\sin (θ + π)}{\cos (θ - π)}

Elianna Bradley

Beginner2023-01-21Added 8 answers

Apply the formulas

\sin (A + B) = \sin A \cos B + \cos A \sin B

and

\cos (A - B) = \cos A \cos B + \sin A \sin B

\Rightarrow \frac{\sin θ \cos π + \cos θ \sin π}{\cos θ \cos π + \sin θ \sin π}

\Rightarrow \frac{\sin θ (- 1) + \cos θ (0)}{\cos θ (- 1) + \sin θ (0)}

\Rightarrow \frac{- \sin θ}{- \cos θ}

Use that identity

\tan β = \frac{\sin β}{\cos β}

\Rightarrow \tan θ

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