Tan({4}theta) = sin({4}theta) divided by 1+cos(4{}theta)

Your syntax is a little unclear, but I can't find any interpretation that makes the identity true. Are you sure you typed it in correctly?

Can you type it in again, using 'x' instead of 'theta', using a carat (^) to indicate an exponent, an asterisk (*) to indicate multiplication, a slash (/) for division, and parentheses around the entire denominator?

Right now, I read your question as either

\tan^4{\the}=\frac{\sin^4{\the}}{1+\cos{(4\the)}}

or

\tan{(4\the)}=\frac{\sin{4\the}}{1+\cos^4{\the}

or

\tan{(4\the)}=\frac{\sin{4\the}}{1+\cos{(4\the)}

or

\tan^4{\the}=\frac{\sin^4{\the}}{1+\cos^4{\the}}

Unfortunately, none of those are statements are true.