Prove the derivative of tan(x) and show trig identities

How to find the derivative of tan(x) .
1st apply tan x as a function in terms of sin and cos.
then apply the quotient rule
the answer before simplification can be shown by either splitting the fractions or by substituting the most famous of trig identities , sin^2 x + cos^2 x =1 .
the answers will show either
sec^2 x
1+tan^2 x
and we see sec^2 = 1 + tan^2 x which is equivalent too tan^2 x = sec^2 x -1
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