Question

(cos 0° + sin 30° + sin 45°) (sin 90° + cos 60° − cos 45°) = ?
(a) $\frac{5}{6}$
(b) $\frac{5}{8}$
(c) $\frac{3}{5}$
(d) $\frac{7}{4}$

Answer 1

(d) $\frac{7}{4}$

$$\begin{gathered} \left(\cos 0^{\mathrm{o}}+\sin {30}^{\mathrm{o}}+\sin {45}^{\mathrm{o}}\right)\left(\sin {90}^{\mathrm{o}}+\cos {60}^{\mathrm{o}}-\cos {45}^{\mathrm{o}}\right) \\ =\left(1+\frac{1}{2}+\frac{1}{\sqrt{2}}\right)\left(1+\frac{1}{2}-\frac{1}{\sqrt{2}}\right) \\ =\left(\frac{3}{2}+\frac{1}{\sqrt{2}}\right)\left(\frac{3}{2}-\frac{1}{\sqrt{2}}\right) \\ =\left[{\left(\frac{3}{2}\right)}^2-{\left(\frac{1}{\sqrt{2}}\right)}^2\right]=\left(\frac{9}{4}\right)-\left(\frac{1}{2}\right)=\left(\frac{9-2}{4}\right)=\frac{7}{4} \end{gathered}$$