How do I simplify #(1+tan^2x+sec^2xcot^2x)/(csc^2x+cot^2xcsc^2x)#?

Question

#(1+tan^2x+sec^2xcot^2x) / (csc^2x+cot^2xcsc^2x)#

I tried simplifying terms and it turned into a mega mess. I just need a simple explanation. Thank you!

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Answer 1 · 2018-02-06T01:10:06

#(1+tan^2x+sec^2xcot^2x) / (csc^2x+cot^2xcsc^2x)#

#=(sec^2x+sec^2xcot^2x) / (csc^2x+cot^2xcsc^2x)#

#=(sec^2x(cancel(1+cot^2x)) )/ (csc^2x(cancel(1+cot^2x))#

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

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