Solve for the interval given xE2pi 2pi those are both fract

Solve for the interval given. xE[-2pi, 2pi].

( those are both fractions cosx/ 1 + sinx + 1 + sinx/cosx = 2 ). Thanks please show steps.

cosx 1 + sinx

------ + ------------- =2   

1 + sinx cosx

Solution

cosx/ 1+sinx + 1+sinx/cosx=2

(cos²x + (1+sinx)²)/(1+sinx)cosx=2

(cos²x+sin²x+ 1+2sinx)/(1+sinx)cosx=2

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

2/cosx=2

1/cosx=1

cosx=1

x=0, 2pi