How do you simplify #tan^2x*csc^2x#?

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Answer 1 · 2015-09-20T17:24:54

According to the following rules:

#tanx = sinx/(cosx)#

#cscx= 1/sinx#

I found

#sec^2 x#

#tan^2x . csc^2x#

#sin^2x/(cos^2x) . 1/ (sin^2x) = 1/cos^2x = sec^2x#

Or using the rule : #sin^2x + cos^2x = 1#

you can rearrange it like:

#1/(sin^2x) = (sin^2x + cos^2x) / sin^2x#

#= sin^2x/sin^2x +cos^2x/sin^2x#

#= 1 + tan^2x#