Buktikan identitas trigonometri berikut: [tex]\displaystyle \frac{1+\tan^2 x}{1+\tan x}=\frac{(\tan x-1)(\cot x+\tan x)}{\tan x-\cot x}[/tex] Pembuktian harus d

Materi Trigonometri
[tex] \displaystyle \frac{1+\tan^2 x}{1+\tan x} \\ = \frac{1+\tan^2 x}{1+\tan x} \times \frac{1-\cot x}{1-\cot x} \\ = \frac{1 + \tan^2 x - \cot x - \cot x \tan^2 x}{1 + \tan x - \cot x - \tan x \cot x} \\ = \frac{\tan x \cot x + \tan^2 x - \cot x - \tan x}{1 + \tan x - \cot x - 1} \\ = \frac{(\tan x - 1)(\cot x + \tan x)}{\tan x - \cot x} [/tex]