Question 1143230
Remember that:
{{{sin^2(x)+cos^2(x)=1}}}
and
{{{cos2x = cos^2(x)-sin^2(x)}}}

Now before substituting any value, factor out first the numerator:
{{{sqrt(4(1+cos2x)/(1-cos2x))}}}

Then, now we take the square root of 4 and substitute the equivalent functions:
{{{sqrt(4(sin^2(x)+cos^2(x)+cos^2(x)-sin^2(x))/(sin^2(x)+cos^2(x)-(cos^2(x)-sin^2(x))))}}}

Solve the expression:
1. {{{sqrt(4(cos^2(x)+cos^2(x)))/(sin^2(x)+cos^2(x)-cos^2(x)+sin^2(x)))}}}
2.{{{sqrt(4(2cos^2(x)))/(2sin^2(x)))}}}
3. Now cancel out 2 and you may find the equivalent in the form of {{{cot^2(x)}}}
4. Lastly get the sqrt of the expression {{{sqrt(4 cot^2(x))}}}

ANSWER: {{{2 cot(x)}}}