Certainly! Let's solve the expression:
[tex]\[ -\sin 30^\circ \times \cos 30^\circ + \sin 45^\circ \times \cos 45^\circ \][/tex]
First, we need to determine the values of the sine and cosine functions at the given angles.
1. Calculate [tex]\(\sin 30^\circ\)[/tex] and [tex]\(\cos 30^\circ\)[/tex]:
- [tex]\(\sin 30^\circ = 0.49999999999999994\)[/tex]
- [tex]\(\cos 30^\circ = 0.8660254037844387\)[/tex]
2. Calculate [tex]\(\sin 45^\circ\)[/tex] and [tex]\(\cos 45^\circ\)[/tex]:
- [tex]\(\sin 45^\circ = 0.7071067811865475\)[/tex]
- [tex]\(\cos 45^\circ = 0.7071067811865476\)[/tex]
Now, substitute these values back into the expression:
[tex]\[ -\sin 30^\circ \times \cos 30^\circ + \sin 45^\circ \times \cos 45^\circ \][/tex]
[tex]\[ = -(0.49999999999999994) \times (0.8660254037844387) + (0.7071067811865475) \times (0.7071067811865476) \][/tex]
Next, perform the multiplications:
1. [tex]\(-0.49999999999999994 \times 0.8660254037844387 = -0.43301270189221924\)[/tex]
2. [tex]\(0.7071067811865475 \times 0.7071067811865476 = 0.5000000000000001\)[/tex]
Finally, add the results:
[tex]\[ -0.43301270189221924 + 0.5000000000000001 = 0.06698729810778087 \][/tex]
Therefore, the value of the expression is:
[tex]\[ 0.06698729810778087 \][/tex]
