Question 1130896

Verify the identity, showing your steps 

(tanx+cosx)/(sinx) = secx+cotx
<pre>{{{matrix(1,3, matrix(1,3, tan (x), "+", cos (x))/sin (x), "=", highlight(highlight(matrix(1,3, sec (x), "+", cot (x)))))}}}
We now focus on just the left-side of equation in order to prove it equal to the right-side
{{{matrix(1,3, sin (x)/cos (x), "+", cos (x))/sin (x))}}} ------------ Substituting {{{matrix(1,3, sin (x)/cos (x), for, tan (x))}}}
{{{matrix(1,5, sin (x)/cos (x), "+", cos (x), "÷", sin (x))}}} --- Making the expression less complex
{{{matrix(1,5, sin (x)/cos (x), "+", cos (x), "*", 1/sin (x))}}}
{{{matrix(1,3, matrix(1,5, sin (x), "+", cos (x), "*", cos (x))/cos (x), "*", 1/sin (x))}}}
{{{matrix(1,3, matrix(1,3, sin (x), "+", cos^2 (x))/cos (x), "*", 1/sin (x))}}}
{{{matrix(1,3, sin (x), "+", cos^2 (x))/cos (x)sin (x)}}}
{{{matrix(1,3, sin (x)/cos (x)sin (x), "+", cos^2 (x)/cos (x)sin (x))}}} ------- Separating expressions
{{{matrix(1,3, 1cross(sin (x))/cos (x)cross(sin (x)), "+", cos (x)cross(cos^2 (x))/cross(cos (x))sin (x))}}} ---- Canceling expressions
{{{matrix(1,3, highlight(highlight(matrix(1,3, sec (x), "+", cot (x)))), "=", highlight(highlight(matrix(1,3, sec (x), "+", cot (x)))))}}} ------- Replacing {{{system(matrix(1,3, 1/cos (x), with, sec (x)), AND, matrix(1,3, cos (x)/sin (x), with, cot (x)))}}} on LEFT-SIDE