Question 433312
{{{sinx/(2(1+cosx))+sinx/(2(1-cosx))=cscx}}}
Multiplying by the conjugate is sometimes a good way to start.
{{{((2(1-cosx))/(2(1-cosx)))*(sinx/(2(1+cosx)))+(sinx/(2(1-cosx)))*((2(1+cosx))/(2(1+cosx)))=cscx}}}
{{{((2-2cosx)/(2-2cosx))*(sinx/(2+2cosx))+(sinx/(2-2cosx))*((2+2cosx)/(2+2cosx))=cscx}}}
{{{((2sin(x)-2sin(x)cos(x))/(4-4cos^2(x)))+((2sin(x)+2sin(x)cos(x))/(4-4cos^2(x)))=cscx}}}
{{{(2sin(x)-2sin(x)cos(x)+2sin(x)+2sin(x)cos(x))/(4-4cos^2(x))=cscx}}}
{{{(2sin(x)+2sin(x))/(4-4cos^2(x))=cscx}}}
{{{(4sin(x))/(4-4cos^2(x))=cscx}}}
{{{(4sin(x))/(4(1-cos^2(x)))=cscx}}}
{{{(sin(x))/(1-cos^2(x))=cscx}}}
{{{(sin(x))/(sin^2(x))=cscx}}}
{{{1/(sin(x))=cscx}}}
{{{cscx=cscx}}}
That was the hardest thing I ever had to type on here.  I hope you understand it!