Show that : `(1+ tan\ theta/2)/(1-tan\ theta/2) = (1+sin theta)/(cos theta) = tan (pi/4 + theta/2)`

Show that (1+tan .theta/2)/(1-tan. theta/2)=(1+sintheta)/(cos theta)=tan(pi/4+theta/2)

Show that (1+tan .theta/2)/(1-tan. theta/2)=(1+sintheta)/(cos theta)=tan(pi/4+theta/2)

Prove that (1+tan theta)/(1-tan theta) = (1 - sin 2 theta)/(cos 2 theta) .

Prove that (1+sin 2theta)/(1-sin 2theta) = ((1+tan theta)/(1-tan theta))^2

Prove that (1+ tan^4 theta)/(1+ tan^2 theta) = sec ^2 theta-2 sin^2theta

Show that, (sin theta)/(cos 3 theta) + (sin 3 theta)/(cos 9 theta) + (sin 9 theta)/(cos 27 theta) = 1/2 ( tan 27 theta - tan theta).

Show that ((tan theta+sec theta-1)/(tan theta-sec theta +1))=(1+sin theta)/(cos theta) .

Show that (tan theta+sec theta -1)/(tan theta - sec theta +1)=(1 + sin theta)/(cos theta)

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

cos theta(tan theta+2)(2tan theta+1)=2sec theta+5sin theta