Question

Proof:
cos2x-1/cosx=-tanxsin

Answer 1

(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

Answer 2

`\cos^(2) x + \sin^(2) x = 1`

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


So:

`(\cos^(2)x-1)/(\cos x)=-\tan x\sin x \Rightarrow (\cos^(2)x-\left(\cos^(2)x + \sin^2 x\right))/(\cos x)=-\tan x\sin x \Rightarrow[tex](-\sin^2x)/(\cos x)=-\tan x\sin x \Rightarrow (-\sin x \sin x)/(\cos x)=-\tan x\sin x \Rightarrow`[/tex]


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