(ii)Prove that `tan(pi/4-theta)=(1-tan theta)/(1+tan theta)`

Prove that tan((pi)/(4)+theta)-tan((pi)/(4)-theta)=2tan2theta .

Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove that (tan^(2)2theta-tan^(2)theta)/(1-tan^(2)2thetatan^(2)theta)=tan3thetatantheta .

Show that the equation of the line passing through the origin and making an angle theta with the line y = mx + c is y/x = (m + tan theta)/(1- m tan theta) or y/ x = (m-tan theta)/(1 + m tan theta)

Prove that (tan5theta+tan3theta)/(tan5theta-tan3theta)=4cos2thetacos4theta

Consider the trigonometric expression sin(2A)/(1-cos 2A) amd sin(2A)/(1+cos 2A) .(iii)Prove that (1-cos theta)/sin theta=tan (theta/2)=(sin theta)/(1+cos theta) .

Prove that (cos2theta)/(1+sin2theta)=tan(pi//4-theta)

Prove that (sin2theta)/(1+cos2theta)=tantheta

Prove that (sin2theta)/(1-cos2theta)=cottheta

Prove that tantheta+tan(60^(@)+theta)+tan(120^(@)+theta)=3tan3theta .