Question 1156990

Write the trigonometric expression in terms of sine and cosine, and then simplify.
 
sin(θ) − csc(θ)
_______________
    cos(θ)
<pre>{{{(sin (theta) - csc (theta))/cos (theta)}}} =====> {{{(sin (theta) - 1/sin (theta))/cos (theta)}}} =====> {{{((sin^2 (theta) - 1)/sin (theta))/cos (theta)}}}, or {{{(sin^2 (theta) - 1)/sin (theta))}}} ÷ {{{cos (theta)}}} =====>  {{{matrix(1,3, (sin^2 (theta) - 1)/sin (theta), "*", 1/cos (theta))}}}
{{{matrix(1,3, (- cos^2 (theta))/sin (theta), "*", 1/cos (theta))}}} ----- Substituting {{{matrix(1,3, - cos^2 (theta), for, sin^2 (theta) - 1)}}}
{{{matrix(1,3, (- cos (theta)cross((- cos^2 (theta))))/sin (theta), "*", 1/cross(cos (theta)))}}} =====> {{{highlight_green(matrix(1,3, - cos (theta)/sin (theta), "====>", highlight(- cot (theta))))}}}