If `cosec theta+cottheta=(a-1)/(a+1)` where `a!=-1,1,0` then find `sin theta` and `tan theta`

Explanation

`cosec theta + cot theta = (a-1)/(a+1)->(1)`

We know, `cosec^2 theta - cot^2theta = 1`

`=>(cosec theta + cot theta )(cosec theta - cot theta) = 1`

`=> (cosec theta - cot theta) = 1/(cosec theta + cot theta)`

`=> cosec theta - cot theta = (a+1)/(a-1)->(2)`

Adding (1) and (2),

`=>cosec theta + cot theta + cosec theta - cot theta = (a-1)/(a+1)+(a+1)/(a-1)`

`=>2cosec theta = ((a-1)^2+(a+1)^2 )/(a^2-1)`

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