Question

tanx (cotx + tanx) = tanx cotx + tan2x = 1+tan2x = sec2x Why does tanx cotx equal to 1?

Answer 1

\[\huge \color{orangered}{\tan x}\cdot\color{royalblue}{\cot x} \qquad = \qquad \color{orangered}{\frac{\sin x}{\cos x}}\cdot \color{royalblue}{\frac{\cos x}{\sin x}}\]See how the trig functions will cancel out? :)

Answer 2

Maybe cancel out is the wrong word. When I say cancel out, I actually mean, they'll divide to give us 1.

E.g.\[\large \frac{\sin x}{\sin x}=1\]

Answer 3

Or even more simply than that, you could use this identity,\[\large \cot x=\frac{1}{\tan x}\]Which would give us this,\[\huge \color{orangered}{\tan x}\cdot\color{royalblue}{\cot x} \qquad = \qquad \color{orangered}{\tan x}\cdot \color{royalblue}{\frac{1}{\tan x}}\]

Answer 4

got it! thanks