How do you simplify $\frac{sin (θ + π)}{cos (θ - π)}$ $sin(theta+pi)/cos(theta-pi)$ ?

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How do you simplify $\frac{sin (θ + π)}{cos (θ - π)}$ $sin(theta+pi)/cos(theta-pi)$ ?

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Answer 1 · 2016-12-07T03:37:05

This simplifies to $tan θ$ $tantheta$ .

Explanation:

Use the formulas $sin (A + B) = sin A cos B + cos A sin B$ $sin(A + B) = sinAcosB + cosAsinB$ and $cos (A - B) = cos A cos B + sin A sin B$ $cos(A - B) = cosAcosB + sinAsinB$ .

$\Rightarrow \frac{sin θ cos π + cos θ sin π}{cos θ cos π + sin θ sin π}$ $=>(sinthetacospi + costhetasinpi)/(costhetacospi + sinthetasinpi)$

$\Rightarrow \frac{sin θ (- 1) + cos θ (0)}{cos θ (- 1) + sin θ (0)}$ $=>(sintheta(-1) + costheta(0))/(costheta(-1) + sin theta(0))$

$\Rightarrow \frac{- sin θ}{- cos θ}$ $=> (-sintheta)/(-costheta)$

Use the identity that $tan β = \frac{sin β}{cos β}$ $tanbeta = sinbeta/cosbeta$ .

$\Rightarrow tan θ$ $=> tantheta$

Hopefully this helps!

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How do you simplify $\frac{sin (θ + π)}{cos (θ - π)}$ $sin(theta+pi)/cos(theta-pi)$ ?

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