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

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Answer 1 · 2017-03-09T02:07:00

$csc^2x$

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

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

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

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

Use $secx = 1/cosx$ and $cotx = cosx/sinx$ .

$(cos^2x/sin^2x)(1/cos^2x)$

$1/sin^2x$

Use $cscx = 1/sinx$ .

$csc^2x$

Hopefully this helps!

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