Determine the solutions of the equation cosx/1+sinx + 1+sinx/cosx = 2 on the interval 0< x < 2pi

Answer 1

by observation after solving

if cos(x)=1, then sin(x)=0 and equation is solved

have cos²(x)+1+2sin(x)+sin²(x)=2cos(x)+2cos(x)sin(x)

same as

2+2sin(x)=2cos(x)+2cos(x)sin(x)

means cos(x)=1

happens once per cycle,

at x=zero, at x=2*pi, at x=-2*pi, ....

the problem probably means to specify 0≤x<2*pi

Answer 2

Multiply both sides of equation by LCD, cos x (1 - sin x).

Then simplify.