Solve for x in the equation. Trig function. Please help 10 POINTS!

Solve for x in the equation within the domain of 0
1+sinx.....cosx
---------- + --------- = 4
cosx......1+sinx

I'm totally stuck I have no idea what to do. Any help will be appreciated. Thank you very much.

First thing is to get rid of the fractions by multiplying by cos(x) ( 1 + sin(x)) on both sides. Then let's see what we have.

(1 + sin x)^2 + (cos x)^2 = 4 cosx( 1 + sin x)

1 + 2 sin(x) + sin^2(x) + cos^2(x) = 4 cosx( 1 + sin x)

And actually it simplifies very nicely.

1 + 2 sin(x) + 1 = 4 cos(x) (1 + sin x)

2 + 2 sin(x) = 4 cos(x)(1 + sin x)

Divide both sides by (1 + sin x).

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