How do you simplify sin(theta+pi)/cos(theta-pi)?

1 Answer
Noah G
Dec 7, 2016

This simplifies to tantheta.

Explanation:

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

=>(sinthetacospi + costhetasinpi)/(costhetacospi + sinthetasinpi)

=>(sintheta(-1) + costheta(0))/(costheta(-1) + sin theta(0))

=> (-sintheta)/(-costheta)

Use the identity that tanbeta = sinbeta/cosbeta.

=> tantheta

Hopefully this helps!

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