When cos(x) + sin(x) = 0 I can see how cos(x) cannot equal 0.
But when written as cos(x)[1 + tan(x)] = 0 cos(x) can be 0?
Could someone please try to explain this to me
Hello, kinhew93!
$\displaystyle \text{When }\,\cos x + \sin x \:=\:0,\,\text{ I can see that }\cos x \ne 0$
$\displaystyle \text{But when written as: }\,\cos x(1 + \tan x) \:=\:0,\: \cos x\text{ can be 0.}$
$\displaystyle \text{Could someone please try to explain this to me?}$
We have: .$\displaystyle \sin x \:=\:-\cos x$
. . . . . . . . $\displaystyle \frac{\sin x}{\cos x} \:=\:-1$ . . . You are right: $\displaystyle \cos x \ne 0$
. . . . . . . . $\displaystyle \tan x \:=\:-1$
Therefore: n . $\displaystyle x \:=\:-\tfrac{\pi}{4} + \pi n$