Simplify $\frac{{cot}^{2} x}{1 + {cot}^{2} x}$ $cot^2x/(1+cot^2x)$ ?

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Answer 1 · 2016-11-27T16:30:54

Please see below.

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

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

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

= $\frac{{cos}^{2} x}{{sin}^{2} x} \times \frac{{sin}^{2} x}{1}$ $cos^2x/sin^2x xxsin^2x/1$

= $cos^2x/cancel(sin^2x) xxcancel(sin^2x)/1$

= $cos^2x$

Simplify cot^2x/(1+cot^2x)cot2x1+cot2xcot^2x/(1+cot^2x)?