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!