# How do you simplify cot x xx sin x?

Aug 17, 2016

$\frac{\cos x}{\sin x} \times \sin x$

=$\cos x$

#### Explanation:

All of the 6 trig ratios can be expressed in terms of $\sin \theta$ and / or $\cos \theta$

$\tan \theta = \frac{\sin \theta}{\cos \theta} \text{ } \frac{\frac{o}{h}}{\frac{a}{h}} = \frac{o \times h}{a \times h} = \frac{o}{a}$

$\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}$

$\sec \theta = \frac{1}{\cos \theta}$

$\cos e c \theta = \frac{1}{\sin \theta}$

$\cot x \times \sin x$

=$\frac{\cos x}{\cancel{\sin x}} \times \cancel{\sin} x$

=$\cos x$