How do you use the fundamental identities to simplify $\frac{1 - {sin}^{2} x}{{csc}^{2} x - 1}$ $(1-sin^2x)/(csc^2x-1)$ ?

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Answer 1 · 2017-02-04T17:34:49

$\frac{1 - {sin}^{2} x}{{csc}^{2} x - 1} = {sin}^{2} x$ $(1-sin^2x)/(csc^2x-1)=sin^2x$

$\frac{1 - {sin}^{2} x}{{csc}^{2} x - 1}$ $(1-sin^2x)/(csc^2x-1)$

= $\frac{{cos}^{2} x}{1 + {cot}^{2} x - 1}$ $cos^2x/(1+cot^2x-1)$

= $\frac{{cos}^{2} x}{{cot}^{2} x}$ $cos^2x/cot^2x$

= $\frac{{cos}^{2} x}{\frac{{cos}^{2} x}{{sin}^{2} x}}$ $cos^2x/(cos^2x/sin^2x)$

= ${cos}^{2} x \times \frac{{sin}^{2} x}{{cos}^{2} x}$ $cos^2x xx sin^2x/cos^2x$

= ${sin}^{2} x$ $sin^2x$

How do you use the fundamental identities to simplify 1−sin2xcsc2x−1(1-sin^2x)/(csc^2x-1)?