$\sin 120°\cos 150°-\cos 240°\sin 330°=$

Solve the expression: sin 120° * cos 150° - cos 240° * sin 330°

Step 1: Apply Trigonometric Identities

The given expression is:

sin 120° * cos 150° - cos 240° * sin 330°    

We recognize that this is in the form of the sine addition and subtraction formulas. Specifically, we can apply the following identities:

• sin(A + B) = sin A * cos B + cos A * sin B
• sin(A - B) = sin A * cos B - cos A * sin B

Thus, the expression becomes:

sin(120° + 30°) * cos(150° + 60°) - cos(240° - 30°) * sin(330° - 360°)    

Step 2: Evaluate the Sine and Cosine Functions

Now we need to evaluate the sine and cosine of the angles:

• sin(120°) = √3 / 2
• cos(150°) = -√3 / 2
• cos(240°) = -1/2
• sin(330°) = -1/2

Substituting these values into the expression:

sin 120° * cos 150° - cos 240° * sin 330°       

= (√3 / 2) * (-√3 / 2) - (-1/2) * (-1/2)    

Step 3: Simplify the Expression

We now simplify the expression:

= -3/4 - 1/4        

= -4/4        

= -1    

Final Answer:

The value of the expression is: -1

Conclusion

Thus, by applying the appropriate trigonometric identities and simplifying the expression step by step, we find that the value of sin 120° * cos 150° - cos 240° * sin 330° is -1.

Note: Throughout this process, we used the value of sin 120° in several steps to simplify the problem.