Given $\cos^2 x = 2 \sin x \cos x$, why can't I cancel $\cos x$ to get $\cos x = 2 \sin x$? If I have a function where I know $\cos^2 x = 2 \sin x \cos x$. Why can I not cross out $\cos x$ on both sides, because I get different values for $\cos x = 2 \sin x$?

You may not divide the two members of an equation by $0$. So you can handle the problem with case analysis:


*

*if $\cos x=0$, the equation holds;

*else if $\cos x\ne0$, the equation can be reduced to $\cos x=2\sin x$.
Now you solve the two cases independently.
