Question 1155878
<pre>
It makes no sense to say "solve" a fraction.  The word is "simplify".
There is a lady on here who will "get you told" if you use improper
words.  So let's simplify, not "solve", the trigonometric expression.

{{{(tan^""(x) + cot^""(x))/sec^2(x)}}} 

{{{matrix(1,3,

tan^""(x) + cot^""(x),(""*"")/(""*""),sec^2(x))}}}

{{{matrix(1,3,

(sin(x)/cos(x) + cos(x)/sin(x)),(""*"")/(""*""),1/cos^2(x))}}}

Get LCD on the left, invert and change to multiplication on the right:

{{{matrix(1,3,

(sin^2(x)+cos^2(x))/(cos^""(x)sin^""(x)),""*"",cos^2(x)/1^"")}}}

Use Pythagorean identity on top

{{{matrix(1,3,
1^""/(cos^""(x)sin^""(x)),""*"",cos^2(x)/1^"")}}}

Cancel the cos(x) into the cos²(x) and get cos(x) on top

{{{matrix(1,3,
1^""/(cross(cos^""(x))sin^""(x)),""*"",cos^cross(2)(x)/1^"")}}}

{{{cos^""(x)/sin^""(x)}}}

{{{cot^""(x)}}}

Edwin</pre>