Question 1205416
<pre>
I am using the fundamental identities to try to verify the following equation. It is a true statement but I find myself a little lost, probably on something basic algebra.

I primarily work on the left side and haven't really worked on the right side.

I know an identity could be verified by using many different methods, which is why the book I am using doesn't explain the process in the answers. So, your manner of verification may differ than what I am doing. Nevertheless, I'd appreciate any help.

In any case, here is the statement to be verified.

1 + sin theta/cot^2 theta = sin theta/csc theta - 1

Thank you very much for your help.

Sir Edwin manipulated the right side to match the left. Hence, I will do the same to the LEFT-SIDE to match the right side.

  {{{matrix(1,3, highlight((1 + sin (theta))/cot^2 (theta)), "=", highlight(highlight_green(highlight(sin (theta)/(csc (theta) - 1)))))}}}

{{{highlight((1 + sin (theta))/(csc^2 (theta) - 1)))}}} ----- Substituting {{{csc^2 (theta) - 1}}} for {{{cot^2 (theta)}}}

{{{highlight((1 + sin (theta))/((csc (theta) - 1)(csc (theta) + 1)))}}} ----- Factoring {{{csc^2 (theta) - 1}}} in denominator

{{{highlight((1 + sin (theta))/((csc (theta) - 1)(1/sin (theta) + 1)))}}} --- Substituting {{{matrix(1,5, 1/sin (theta), for, csc (theta), in, csc (theta) + 1)}}}

{{{highlight((1 + sin (theta))/((csc (theta) - 1)((1 + sin (theta))/sin (theta))))}}}

{{{highlight((1 + sin (theta))/((csc (theta) - 1)(1 + sin (theta))/sin (theta))))}}} 
 
{{{highlight((1 + sin (theta)) * sin (theta)/(csc (theta) - 1)(1 + sin (theta))))}}} 

{{{highlight(cross((1 + sin (theta))) * sin (theta)/(csc (theta) - 1)cross((1 + sin (theta)))))}}} 
 
            {{{matrix(1,3, highlight((sin (theta))/(csc (theta) - 1)), "=", highlight(highlight_green(highlight(sin (theta)/(csc (theta) - 1)))))}}}</pre>