# Proving a trigonometric identity (I'm a newbie)

Why does $$-\frac{\cos^2 x}{\sin x}= -\cos x\cot x?$$ Sorry for the dumb question.

• break up the $-cos^2(x)$ into a product of 2 cosines. then use a trig definition. – MathHype Mar 28 '15 at 19:29
• Remember that $a^2 = aa$, and that $\frac{ab}{c} = \frac{a}{c}b = a\frac{b}{c}$. – Miguelgondu Mar 28 '15 at 19:40

Look at my comment above. $$\frac{-\cos^2(x)}{\sin(x)}\rightarrow \frac{-\cos(x)*{\color{red} {\cos(x)}}}{\color{red}{\sin(x)}} \rightarrow -\cos(x)\cot(x)$$
hint : $\cot(x)=\frac{cos(x)}{\sin(x)}$
$-\frac{\cos^2(x)}{\sin(x)}=-\frac{\cos(x)\cdot \cos(x)}{\sin(x)}=-\cos(x)\cdot\frac{\cos(x)}{\sin(x)}=-\cos(x)\cot(x)$