How do you simplify ${cot}^{2} x ({tan}^{2} x + 1)$ $cot^2x(tan^2x+ 1)$ ?

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Answer 1 · 2017-03-09T02:07:00

${csc}^{2} x$ $csc^2x$

We start by factoring out a ${cot}^{2} x$ $cot^2x$ .

${cot}^{2} x ({tan}^{2} x + 1)$ $cot^2x(tan^2x + 1)$

Use the identity ${tan}^{2} x + 1 = {sec}^{2} x$ $tan^2x + 1 = sec^2x$ .

${cot}^{2} x ({sec}^{2} x)$ $cot^2x(sec^2x)$

Use $sec x = \frac{1}{cos x}$ $secx = 1/cosx$ and $cot x = \frac{cos x}{sin x}$ $cotx = cosx/sinx$ .

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

$\frac{1}{{sin}^{2} x}$ $1/sin^2x$

Use $csc x = \frac{1}{sin x}$ $cscx = 1/sinx$ .

${csc}^{2} x$ $csc^2x$

Hopefully this helps!

How do you simplify cot^2x(tan^2x+ 1)cot2x(tan2x+1)cot^2x(tan^2x+ 1)?