Question

Evaluate the following:

sin 60° cos 30° – cos 60° sin 30°

Answer 1

Given: sin 60° cos 30° – cos 60° sin 30°

Use the sine subtraction identity: sin A cos B – cos A sin B = sin(A – B), so the expression = sin(60° – 30°) = sin 30°.

Or evaluate directly:

`sin 60^circ = sqrt(3)/2` and `cos 30^circ = sqrt(3)/2`,

So `sin 60^circ · cos 30^circ = (sqrt(3)/2)(sqrt(3)/2) = 3/4`.

`cos 60^circ = 1/2` and `sin 30^circ = 1/2`,

So `cos 60^circ·sin 30^circ = (1/2)(1/2) = 1/4`.

Difference = `3/4 - 1/4 = 1/2`.

sin 60° cos 30° – cos 60° sin 30° = `1/2`.