Question

simplify
(1+sin(-x)/1+cos(-x))-(1-sin(-x)/1-cos(-x))

Answer 1

\[\frac{ 1+\sin(-x) }{ 1+\cos(-x) }-\frac{ 1-\sin(-x) }{ 1-\cos(-x) }\]

Answer 2

Sine and cosine are odd/even functions, respectively, which means
\[\sin(-x)=-\sin x\\
\cos(-x)=\cos x\]
So,
\[\frac{ 1+\sin(-x) }{ 1+\cos(-x) }-\frac{ 1-\sin(-x) }{ 1-\cos(-x) }=\frac{ 1-\sin x }{ 1+\cos x }-\frac{ 1+\sin x }{ 1-\cos x }\]