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tantheta /(1-cottheta ) + cottheta/(1-ta...

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

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LHS `(tanθ​)/(1−cotθ)+(cotθ​)/(1−tanθ)`
`=(​tanθ)/(1−1/(tanθ))​+(1/(tanθ)​​)/(1−tanθ)`
`=(tan^2θ​)/(tanθ−1)-1/(tanθ(tanθ-1))`
`=(tan^3θ−1​)/(tanθ(tanθ−1))` ...
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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

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(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