Prove that `cot(theta/2)-tan(theta/2)=2cot theta`

Prove that cot theta-tan theta=2cot 2 theta .

Prove that sin(2theta)/(1-cos2theta)=cot theta

Prove that cot 2 theta + tan theta = cosec 2 theta

Prove that (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta) = (sec theta cosec theta +1)

Prove that: cotthetacot2theta+cot2thetacot3theta+2=cottheta(cottheta-cot3theta)

Solve the equation cot((theta )/(2))-"cosec"((theta)/2)=cot theta

Prove that ((1+cot theta +tan theta)(sin theta - cos theta))/(sec ^3 theta -cosec^3 theta) = sin^2 theta cos^2 theta.

Solve tan5theta=cot2theta

The base of a triangle is divided into three equal parts. If theta_(1), theta_(2), theta_(3) be thw angles subtended by these parts at the vertex, then prove that (cot theta_(1) +cot theta_(2) ) (cot theta_(2)+ cot theta_(3))=4 cosec ^(2) theta _(2)

Prove that : (cos theta)/(1-tan theta) + (sin theta)/(1-cot theta) = sin theta + cos theta