`tantheta /(1-cottheta ) + cottheta/(1-tan theta)= 1+sectheta*cosectheta`

Prove that : (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+sectheta" cosec "theta

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

(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+tantheta+cottheta=sectheta"cosec"theta+1

(tantheta)/(1-cottheta)+(cottheta)/(1-tantheta) is equal to -

1+cottheta="cosec"theta

Prove that : sintheta(1+tantheta)+costheta(1+cottheta)=cosectheta+sectheta

("sin"theta)/(1-costheta)+("tan"theta)/(1+costheta)=secthetacosectheta+cottheta

(1+cottheta-cosectheta)(1+tantheta+sectheta)=?

(i) "sin"theta cot theta + "sin"theta cosectheta = 1+ costheta (ii) sectheta(1-"sin"theta) (sectheta+tantheta)=1 (iii) "sin"theta(1+"tan"theta)+costheta(1+cottheta)=sectheta+cosectheta

If theta epsilon (0, pi/2) then the value of |((sintheta+cosectheta)^2, (sintheta- cosectheta)^2,1 ),((costheta+sectheta)^2, (costheta-sectheta)^2, 1),((tantheta+cottheta)^2, (tantheta-cottheta)^2, 1)|= (A) sintheta+costhetas+tantheta (B) 1 (C) 0 (D) 4