# How do you prove that sinthetacostheta=cottheta is not an identity by showing a counterexample?

Feb 17, 2017

we just need one value to show this.

#### Explanation:

$\text{take "theta=45^0 " and work out teh approriate values}$

$L H S , \text{ } \sin 45 \times \cos 45 = \frac{\sqrt{2}}{2} \times \frac{\sqrt{2}}{2} = \frac{2}{4} = \frac{1}{2}$

$R H S \cot 45 = \frac{1}{\tan} 45 = \frac{1}{1} = 1$

$\therefore \sin 45 \cos 45 \ne \cot 45$