Does $\tan x\cdot \cos x$ equal $\sin x$? Is it true that $\tan x\cdot \cos x = \sin x$? If I put $x=30$ in my calculator then I don't get the same answer as $\sin 30$, why is this? Don't the two cosines cancel out? I'm probably missing something really stupid here.

Without doubt,
$$\tan30°\cdot\cos30°=\frac1{\sqrt3}\cdot\frac{\sqrt3}2=\frac12=\sin30°$$
$$0.57735026919\cdots\times0.86602540378\cdots=0.5$$
