Given:
The objective is to find the exact value of sin(285°).
Step-by-step explanation:
The given value can be rewritten as,

The general formula of sin(a+b) is,

Here A = 240° and B = 45°.
Using equation (2), the equation (1) can be written as,

Since it is known that,

Now, equation (3) can be written as,

On plugging the trigonometric values in equation (4),
![\begin{gathered} \sin (240\degree+45\degree)=(-\frac{\sqrt[]{3}}{2}*\frac{1}{\sqrt[]{2}})+(\frac{1}{\sqrt[]{2}}*-(1)/(2)) \\ =-\frac{\sqrt[]{3}}{2\sqrt[]{2}}-\frac{1}{2\sqrt[]{2}} \\ =-\frac{\sqrt[]{3}}{2\sqrt[]{2}}*\frac{\sqrt[]{2}}{\sqrt[]{2}}-\frac{1}{2\sqrt[]{2}}*\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =-\frac{\sqrt[]{6}}{4}-\frac{\sqrt[]{2}}{4} \\ =\frac{-\sqrt[]{6}-\sqrt[]{2}}{4} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/exxgsz64q0ia1peml9ekum58066exsbdxk.png)
Hence, option (1) is the correct answer.