Show that `e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.`

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

If "cosec"theta=2 , show that (cottheta+(sintheta)/(1+costheta))=2 .

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

let z1, z2,z3 be vertices of triangle ABC in an anticlockwise order and angle ACB = theta then z_2-z_3 = (CB)/(CA)(z_1-z3) e^itheta . let p point on a circle with op diameter 2 points Q & R taken on a circle such that angle POQ & QOR= theta if O be origin and PQR are complex no. z1, z2, z3 respectively then z_2/z_1 = (A) e^(itheta) cos theta (B) e^(itheta) cos 2theta (C) e^(-itheta) cos theta (D) e^(2itheta) cos 2theta

Find the value of ((1-tantheta)/(1-cottheta))^2

The value of sqrt((1+costheta)/(1-costheta)) is (a) cottheta-cos e c\ theta (b) cos e c\ theta+cottheta (c) cos e c^2theta+cot^2theta (d) (cottheta+cos e c\ theta)^2

Prove the trigonometric identities: (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+tantheta+cottheta

Prove that: {1+cottheta-s e c(pi/2+theta)}{1+cottheta+s e c(pi/2+theta)}=2cottheta

Prove that: sqrt((1+costheta)/(1-costheta))=cos e ctheta+cottheta .

Prove that : (1+cottheta+"cosec"theta)(1+cottheta-"cosec"theta)=2cottheta