Question

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

Answer 1

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!