Question 896455
I will take theta as x

(sinx + 1)/(1+ cosx) + cosx/sinx = 2cosecx

(sinx(sinx+1) + cosx(1+cosx))/sinx*(1+cosx) =

((sinx)^2 + sinx + (cosx)^2 + cosx)/sinx*(1+cosx)

(sinx + 1 + cosx)/sinx*(1+cosx)

you can separate like this.

sinx/sinx*(1+cosx) + (1+cosx)/sinx*(1+cosx)

1/(1+cosx) + 1/sinx

This doesn't give the given answer 2cosecx. Something went wrong with the question.