How do you simplify the expression $cot^2x/(cscx+1)$ ?

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Answer 1 · 2016-09-21T19:59:33

$cscx-1$

$cot^2x/(cscx+1)$

One of the Pythagorean identities is $1+cot^2x=csc^2$

Rearranging:
$cot^2x=csc^2x-1$

Substitute $csc^2x-1$ into the numerator for $cot^2x$

$(csc^2x-1)/(cscx+1)$

Factor the numerator by difference of squares:

$((cscx+1)(cscx-1))/(cscx+1)$

Cancel the common factor in numerator and denominator:

$cscx-1$

How do you simplify the expression cot^2x/(cscx+1)cot^2x/(cscx+1)?