Question

evaluate cos(225°)

Explanation:

Step1: Use the angle addition formula

$$\cos(225^{\circ})=\cos(180^{\circ} + 45^{\circ})$$
According to the formula $\cos(A + B)=\cos A\cos B-\sin A\sin B$, here $A = 180^{\circ}$ and $B=45^{\circ}$.
So, $\cos(180^{\circ}+45^{\circ})=\cos180^{\circ}\cos45^{\circ}-\sin180^{\circ}\sin45^{\circ}$

Step2: Substitute the values of trigonometric functions

We know that $\cos180^{\circ}=- 1$, $\sin180^{\circ}=0$, $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, $\sin45^{\circ}=\frac{\sqrt{2}}{2}$
Substitute these values into the above formula:
$$\cos(180^{\circ}+45^{\circ})=(-1)\times\frac{\sqrt{2}}{2}-0\times\frac{\sqrt{2}}{2}=-\frac{\sqrt{2}}{2}$$

Answer:

$-\frac{\sqrt{2}}{2}$