the derivative of sin/cos is..
(cos(x)cos(x)-(sin(x)(-sin(x)))/(cos(x))^2
then you can simplify it to..
(cos(x)^2+sin(x)^2)/(cos(x))^2
now cos(x)^2+sin(x)^2=1 and 1/cos(x)^2 is the same as sec(x)^2
make sense?
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