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

1 Answer
Jun 16, 2018

#"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"#