Question

Proof:cos2x-1/cosx=-tanxsin

Answer 1

$\cos^{2} x + \sin^{2} x = 1$

With this info you can exchange 1 and there you got your answer.


So:
$\frac{\cos^{2}x-1}{\cos x}=-\tan x\sin x \Rightarrow \frac{\cos^{2}x-\left(\cos^{2}x + \sin^2 x\right)}{\cos x}=-\tan x\sin x \Rightarrow[tex]\frac{-\sin^2x}{\cos x}=-\tan x\sin x \Rightarrow \frac{-\sin x \sin x}{\cos x}=-\tan x\sin x \Rightarrow$[/tex]

$\left (-\tan x \right)\cdot \sin x = -\tan x \sin x$

Answer 2

(cos² x-1) / cos x = -tg x*sen x
sen²x + cos²x = 1
cos²x - 1 = -sen²x

-sen²x / cos x = - (sen x / cos x)*sen x =
 -sen²x / cos x