SOLUTION: I am stuck on the following question: Solve for x in the equation: (1+sinx)/cosx + cosx/(1+sinx) = 4 for 0<=x<=2pi rads Any help is appreciated Thank You

Algebra ->  Trigonometry-basics -> SOLUTION: I am stuck on the following question: Solve for x in the equation: (1+sinx)/cosx + cosx/(1+sinx) = 4 for 0<=x<=2pi rads Any help is appreciated Thank You      Log On


   

Question 430840: I am stuck on the following question:
Solve for x in the equation: (1+sinx)/cosx + cosx/(1+sinx) = 4 for 0<=x<=2pi rads
Any help is appreciated
Thank You
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x in the equation: (1+sinx)/cosx + cosx/(1+sinx) = 4 for 0<=x<=2pi rads
..
(1+sinx)/cosx + cosx/(1+sinx) = 4
LCD: (cosx)(1+sinx)
(1+sinx)^2+cos^2x=4(cosx)(1+sinx)
1+2sinx+sin^2x+cos^2x=4(cosx)(1+sinx)
sin^2x+cos^2x=1
2+2sinx=4(cosx)(1+sinx)
2(1+sinx)=4(cosx)(1+sinx)
2=4(cosx)
cosx=2/4=1/2
x=pi/3 and 5pi/3 (note: cos positive in quadrants I and IV)