Question 197454
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Solve for x in the equation (1 +sinx/cosx)+(cosx/1+sinx)=4 for 0≤ x ≤ 2π rad.
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        The answers x = pi/6 or 11pi/6 in the post by HyperBrain both are incorrect.

        I came to bring a correct solution.



{{{(1 +sinx)/cosx + cosx/(1+sinx)=4}}}
Multiply both sides by cos x (1+ sin x)
{{{(1 + sin x)^2 + cos^2 (x)=4cos x (1+ sin x)}}}
{{{1+ 2 sin x + sin^2(x) + cos^2 (x)=4cos x (1+ sin x)}}}
{{{2+2sin x=4cos x(1+sin x)}}}
{{{1+ sin x=2cos x(1+sin x)}}}
Divide both sides by 1 + sin x
{{{2 cos x=1}}}
{{{cos x=1/2}}}
There are only two solutions:
x=pi/3 or 5pi/3


Solved correctly.