Question 117
The value of $$(\cos 0^\circ + \sin 45^\circ + \sin 30^\circ) (\sin 90^\circ - \cos 45^\circ + \cos 60^\circ)$$ is
Solution
$$(\cos 0^\circ + \sin 45^\circ + \sin 30^\circ) (\sin 90^\circ - \cos 45^\circ + \cos 60^\circ)=\left(1+\frac{1}{\sqrt{2}}+\frac{1}{2}\right)\left(1-\frac{1}{\sqrt{2}}+\frac{1}{2}\right)=\left(\frac{3}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{3}{2}-\frac{1}{\sqrt{2}}\right)=\frac{9}{4}-\frac{1}{2}=\frac{7}{4}$$
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