Question

The value of $(\cos 0^{\circ }+\sin {45}^{\circ }+\sin {30}^{\circ })(\sin {90}^{\circ }-\cos {45}^{\circ }+\cos {60}^{\circ })$ is

• A. 0
• B. 1
• C. $\frac{7}{4}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{7}{4}$

$(\cos 0^0+\sin {45}^{\circ }+\sin {30}^0)+(\sin {90}^0-\cos {45}^0+\cos {60}^0)$

$\Rightarrow (1+\frac{1}{\sqrt{2}}+\frac{1}{2})(1-\frac{1}{\sqrt{2}}+\frac{1}{2})$

$\Rightarrow (\frac{3}{2}+\frac{1}{\sqrt{2}})(\frac{3}{2}-\frac{1}{\sqrt{2}})$

$\Rightarrow {\left(\frac{3}{2}\right)}^2-{\left(\frac{1}{\sqrt{2}}\right)}^2$

$\Rightarrow \frac{9}{4}-\frac{1}{2}$

$\Rightarrow \frac{9-2}{4}=\frac{7}{4}$

Hence, the answer is $\frac{7}{4}.$