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8. Introduction to Trigonometry
easy
$\sin 60 \sin 45+\cos 60 \cos 45=\ldots \ldots \ldots \ldots$
A
$\sqrt{3}+1$
B
$\frac{\sqrt{3}+1}{2}$
C
$\frac{\sqrt{6}+\sqrt{2}}{4}$
D
$\frac{1}{2}$
Solution
$\sin 60 \sin 45+\cos 60 \cos 45=\frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}}+\frac{1}{2} \cdot \frac{1}{\sqrt{2}}$
$=\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}$
$=\frac{\sqrt{3}+1}{2 \sqrt{2}}=\frac{(\sqrt{3}+1) \times \sqrt{2}}{2 \sqrt{2} \times \sqrt{2}}=\frac{\sqrt{6}+\sqrt{2}}{4}$
Standard 10
Mathematics
