Question

How do you verify the identity `tan(theta+pi/2)=-cottheta`?

Answer 1

`"see explanation"`

Explanation:

`"using the "color(blue)"addition formulae for sin/cos"`

`•color(white)(x)sin(x+y)=sinxcosy+cosxsiny`

`•color(white)(x)cos(x+y)=cosxcosy-sinxsiny`

`tan(theta+pi/2)=(sin(theta+pi/2))/(cos(theta+pi/2))`

`sin(theta+pi/2)=sinthetacos(pi/2)+costhetasin(pi/2)`

`color(white)(xxxxxxxx)=sintheta(0)+costheta(1)=costheta`

`cos(theta+pi/2)=costhetacos(pi/2)-sinthetasin(pi/2)`

`color(white)(xxxxxxxx)=costheta(0)-sintheta(1)=-sintheta`

`tan(theta+pi/2)=costheta/(-sintheta)=-cottheta" as required"`