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Simplify $\sin 45 ° \cos 60 ° - \cos 45 ° \sin 60 °$ .

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\frac{1 - \sqrt{3}}{2 \sqrt{2}}

\frac{\sqrt{3}}{2 \sqrt{2}}

\frac{1 + \sqrt{3}}{2 \sqrt{2}}

0

answer is C.

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Detailed Solution

Given trigonometric expression is,

\sin 45 ° \cos 60 ° - \cos 45 ° \sin 60 °

We know that,

\cos 60 ° = \frac{1}{2}, \sin 45 ° = \frac{1}{\sqrt{2}}, \cos 45 ° = \frac{1}{\sqrt{2}}, and sin 60 ° = \frac{\sqrt{3}}{2}

Then,

\sin 45 ° \cos 60 ° - \cos 45 ° \sin 60 °

= \frac{1}{\sqrt{2}} \times \frac{1}{2} + \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2}

= \frac{1 + \sqrt{3}}{2 \sqrt{2}}

Therefore,

\sin 45 ° \cos 60 ° - \cos 45 ° \sin 60 ° = \frac{1 + \sqrt{3}}{2 \sqrt{2}}

Hence, option (3) is correct.

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