Question

Evaluate the following :
$\left(cose{c}^2{45}^{\circ }se{c}^2{30}^{\circ }\right)(si{n}^2{30}^{\circ }+4co{t}^2{45}^{\circ }-se{c}^2{60}^{\circ })$

Answer 1

Given $\left(cose{c}^2{45}^{\circ }se{c}^2{30}^{\circ }\right)(si{n}^2{30}^{\circ }+4co{t}^2{45}^{\circ }-se{c}^2{60}^{\circ })$

$=({\left(\sqrt{2}\right)}^2\cdot {\left(\frac{2}{\sqrt{3}}\right)}^2)({\left(\frac{1}{2}\right)}^2+4{\left(1\right)}^2-{\left(2\right)}^2)$

$=\left(\frac{8}{3}\right)(\frac{1}{4}+4-4)$

$=\frac{8}{3}\cdot \frac{1}{4}$

$=\frac{2}{3}$