Mathematics

The key is to write $\tan x$ as a ratio and use the quotient rule—this turns a tricky trig derivative into an algebra problem. Once you apply the rule and simplify using $\sin^2 x + \cos^2 x = 1$, you'll see a clean trigonometric identity emerge that's much simpler than the intermediate steps suggest.

The key is to write $\tan x$ as a ratio and use the quotient rule—this turns a tricky trig derivative into an algebra problem. Once you apply the rule and simplify using $\sin^2 x + \cos^2 x = 1$, you'll see a clean trigonometric identity emerge that's much simpler than the intermediate steps suggest.