Question 1075848
<pre>
{{{sin(x)/(1-cos(x))=4tan(x)}}}

We multiply through by 1-cos(x) but if we do we
must rule out the case where the denominator
1-cos(x) would be 0, which would be when cos(x) = 1
which would be x=0°  

{{{sin(x)=4tan(x)(1-cos(x)^"")}}}

We change tan(x) to sin(x)/cos(x)

{{{sin(x)=4(sin(x)/cos(x))(1-cos(x)^"")}}}

Distributing on the right gives:

{{{sin(x)=4sin(x)/cos(x)-4sin(x)^"")}}}

We multiply through by cos(x) but if we do we
must rule out the case where the denominator
cos(x) would be 0, which would be when 
x = 90° or 270°  

{{{sin(x)cos(x)=4sin(x)-4sin(x)cos(x)}}}

We get 0 on the right:

{{{5sin(x)cos(x)-4sin(x)=0}}}

Factor out sin(x)

{{{sin(x)(5cos(x)-4^"")=0}}} 

Setting the first factor = 0,

{{{sin(x)=0}}}

x = 0° or 180° but we have ruled out x=0°,
so the only answer from setting the 
first factor = 0 is 180°

Setting the second factor = 0

{{{5cos(x)-4=0}}}

{{{5cos(x)=4}}}

{{{cos(x)=4/5}}}

Use calculator to get QI answer and
subtract it from 360° to get QIV answer. 
x = 36.86989765° and 323.1301024°

Solutions: 180°, 36.86989765°, 323.1301024°

Edwin</pre>