Question 826394
I guessing you meant
{{{ ((csc^2(x))-(cot^2(x)))/(sec^2(x))}}}
with cot instead of cos. If I am wrong then you will have to re-post your question.<br>
One of the Pythagorean identities is {{{cot^2(x)+1=csc^2(x)}}}. Using this we can substitute in for {{{csc^2(x)}}}:
{{{ ((cot^2(x)+1)-(cot^2(x)))/(sec^2(x))}}}
The cot's cancel:
{{{ 1/(sec^2(x))}}}
One of the Reciprocal identities is that sec and cos are reciprocals of each other. So:
{{{ 1/(sec^2(x))}}}
is equal to:
{{{cos^2(x)}}}