Question

The value of

$co{s}^2\left({45}^0\right)$+$co{s}^4\left({30}^0\right)$+$si{n}^4\left({30}^0\right)$+$si{n}^4\left({60}^0\right)$

• A. $\frac{27}{16}$
• B. $\frac{7}{16}$
• C. $\frac{5}{16}$
• D. $\frac{3}{16}$

Answer 1

The correct option is A $\frac{27}{16}$

$co{s}^2\left({45}^0\right)$+$co{s}^4\left({30}^0\right)$+$si{n}^4\left({30}^0\right)$+$si{n}^4\left({60}^0\right)$
$={\left(\frac{1}{\sqrt{2}}\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^4+{\left(\frac{1}{2}\right)}^4+{\left(\frac{\sqrt{3}}{2}\right)}^4$
$=\frac{1}{2}+\frac{9}{16}+\frac{1}{16}+\frac{9}{16}$
$=\frac{27}{16}$