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I'm pretty clear about the trigonometric identities but I have no idea how to apply them to this question.

If $0^{\circ} \leq x < 90^{\circ}$, then simplify $\tan x\cos x$.

The answer is $\sin x$. But why?

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  • $\begingroup$ Use that $\tan x=\frac{\sin x}{\cos x}$ $\endgroup$ – user84413 Sep 15 '14 at 0:17
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The function $\tan$ is defined by the relation $\tan(x)=\frac{\sin(x)}{\cos(x)}$. Thus, multiplying by $\cos(x)$ will clear the denominator.

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Use the definition of $\tan x$. $$\tan x \cos x = \frac{\sin x}{\cos x}\cos x = \sin x$$

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