sin 420° cos 390° + cos (–660°) sin (–330°) is equal to

To solve this problem, we need to use the properties of sine and cosine functions.

Step 1: Convert the angles to their equivalent within the range of 0° to 360°.

420° is equivalent to 60° because 420 - 360 = 60. 390° is equivalent to 30° because 390 - 360 = 30. -660° is equivalent to 60° because -660 + 720 = 60. -330° is equivalent to 30° because -330 + 360 = 30.

Step 2: Substitute the equivalent angles into the equation.

sin 420° cos 390° + cos (–660°) sin (–330°) = sin 60° cos 30° + cos 60° sin 30°

Step 3: Use the sine and cosine values of 30° and 60°.

sin 60° = √3/2, cos 30° = √3/2, cos 60° = 1/2, sin 30° = 1/2.

Substitute these values into the equation:

(√3/2 * √3/2) + (1/2 * 1/2) = 3/4 + 1/4 = 1.

So, sin 420° cos 390° + cos (–660°) sin (–330°) = 1.