Verify d/dx tan(x) = sec^2 (x) and d/dx cot (x) = -csc^2 (x)

use the quotient rule.

so for d/dx tan(x) = sec^2 (x) would it be

sin(x)/cos(x)=(sec(x)tan(x))^2

the answer is: sin(x)/cos(x)/(sec(x)tan(x))^2= sec^2 (x) (sin(x)/cos(x))- tan(x)*(sec(x)tan(x))^2/(sec^2)^2

and for d/dx cot (x) = -csc^2 (x)

the aswer is

tan(x)/(csc(x)cot(x)^2= -csc^2(x)(tan(x))-(cot(x))((csc(x))cot(x))^2/-csc^2(x)

I am really confused please help. I do not kno how 2 reduce or if this is even right can someone please explain the right answer to me thank you