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Evaluate the following expression:

[tex]-\sin 30^{\circ} \times \cos 30^{\circ} + \sin 45^{\circ} \times \cos 45^{\circ} = ?[/tex]

Sagot :

GinnyAnsweridn
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]
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