Question

Just want to clarify something -

http://prntscr.com/9pultv

Can't I prove that all of these exist?

Answer 1

One of those is not true for all values of \(x\).

Answer 2

write each one out in terms of sin and cos and cancel as appropriate

For example,
\[\cos(x) \tan(x) = \sin(x)\]\[\cancel{\cos(x)}*\frac{\sin(x)}{\cancel{\cos(x)}} = \sin(x)\]\[\sin(x) = \sin(x)\checkmark\]

Answer 3

If I do that, it makes C wrong? @whpalmer4

Answer 4

Exactly!

Answer 5

\[\tan(x)\sec(x)\sin(x) = 1\]\[\frac{\sin(x)}{\cos(x)}*\frac{1}{\cos(x)}*\sin(x) = 1\]but that's the same as \[\tan(x)*\tan(x) = 1\]and that clearly is not always true!