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

If tan theta+tan(60^(@)+theta)+tan(120^(@)+theta)=3, Prove that: (3tantheta-tan^(3)theta)/(1-3tan^(2)theta)=1

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tantheta))^2

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)

If theta=30^@ , verify that: (i) tan2theta=(2tantheta)/(1-tan^2theta) (ii) sin2theta=(2tantheta)/(1+tan^2theta)

Prove that: (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+secthetacos e ctheta

i) Prove that: (1+tan^(2)A)/(1-tan^(2)A) xx (2 cos^(2) A-1)=1 ii) Prove that: (tantheta)/(1+cottheta)+(cottheta)/(1+tantheta) = "cosec"theta.sectheta-1

Prove that : (tan theta)/(sectheta+1)-(tantheta)/(1-sectheta)=2cosec theta

Prove that (1+sectheta-tantheta)/(1+sectheta+tantheta) = (1-sintheta)/(costheta)

Prove that (1+sectheta-tantheta)/(1+sectheta+tantheta) = (1-sintheta)/(costheta)

given that tan(theta_1 + theta_2) = (tantheta_1 + tantheta_2)/(1-tantheta_1*tantheta_2) find (theta_1+theta_2) when tantheta_1 =1/2 , tantheta_2=1/3