Question 1208309
<pre>

1/tan^2pie/8 - 1/sin^2pie/8

Evaluate

Thanks 

1/tan^2<font color = red><s>pie</s></font>pi/8 - 1/sin^2<font color = red><s>pie</s></font>pi/8
{{{1/(tan^(2)(pi/8)) - 1/(sin^(2)(pi/8))}}}
{{{matrix(1,3, 1/(tan^(2)(pi/8)), "=", cot^2(pi/8))}}}       and      {{{matrix(1,3, 1/(sin^(2)(pi/8)), "=", csc^2(pi/8))}}} 
{{{1/(tan^(2)(pi/8)) - 1/(sin^(2)(pi/8))}}} <font color = red><font size = 4><b>then becomes:</font></font></b>{{{cot^2(pi/8) - csc^2(pi/8)}}} 

<font color = red><font size = 5><b>IDENTITY: </font></font></b>{{{matrix(2,3, csc^2(theta) - cot^2(theta), "=", 1, csc^2 (theta), "=", 1 + cot^2(theta))}}}
              Therefore, {{{matrix(1,3, csc^2 (pi/8), "=", 1 + cot^2(pi/8))}}}

{{{matrix(1,3, 1/(tan^(2)(pi/8)) - 1/(sin^(2)(pi/8)), "=", cot^2(pi/8) - csc^2(pi/8))}}}
                             {{{cot^2(pi/8) - (1 + cot^2(pi/8))}}} ----- Substituting{{{1 + cot^2(pi/8)}}} for {{{csc^2 (pi/8)}}}
                             {{{matrix(1,5, cot^2(pi/8) - 1 - cot^2(pi/8), "=", cot^2(pi/8) - cot^2(pi/8) - 1, "=", highlight(- 1))}}}</pre>