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How do you simplify the expression $\frac{1 - csc x}{1 - {csc}^{2} x}$ $(1-cscx)/(1-csc^2x)$ ?

1 Answer

Oct 24, 2016

$\frac{1 - csc (x)}{1 - {csc}^{2} (x)} = \frac{1}{1 + csc (x)}$ $(1-csc(x))/(1-csc^2(x)) = color(green)(1/(1+csc(x)))$

Explanation:

Remember $a^{- b}^2 = (a - b) (a + b)$ $a^-b^2=(a-b)(a+b)$
So
$XXX 1 - {csc}^{2} (x) = (1 - csc (x)) (1 + csc (x))$ $color(white)("XXX")1-csc^2(x)=(1-csc(x))(1+csc(x))$
and
$(1-csc(x))/(1-csc^2(x))=cancel(1-csc(x))/(cancel(""(1-csc(x)))(1+csc(x))$

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