How do I simplify (1+tan^2x+sec^2xcot^2x)/(csc^2x+cot^2xcsc^2x)1+tan2x+sec2xcot2xcsc2x+cot2xcsc2x?

(1+tan^2x+sec^2xcot^2x) / (csc^2x+cot^2xcsc^2x)1+tan2x+sec2xcot2xcsc2x+cot2xcsc2x

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

1 Answer
Feb 6, 2018

(1+tan^2x+sec^2xcot^2x) / (csc^2x+cot^2xcsc^2x)1+tan2x+sec2xcot2xcsc2x+cot2xcsc2x

=(sec^2x+sec^2xcot^2x) / (csc^2x+cot^2xcsc^2x)=sec2x+sec2xcot2xcsc2x+cot2xcsc2x

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

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

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