Question

Question 1 (v)
Evaluate the following:
(v) $\frac{5co{s}^2{60}^{\circ }+4se{c}^2{30}^{\circ }-ta{n}^2{45}^{\circ }}{si{n}^2{30}^{\circ }+co{s}^2{30}^{\circ }}$

Answer 1

(v) $\frac{5co{s}^2{60}^{\circ }+4se{c}^2{30}^{\circ }-ta{n}^2{45}^{\circ }}{si{n}^2{30}^{\circ }+co{s}^2{30}^{\circ }}$
$=\frac{5(\frac{1}{2}{)}^2+4(\frac{2}{\sqrt{3}}{)}^2-1^2}{(\frac{1}{2}{)}^2+(\frac{\sqrt{3}}{2}{)}^2}$
$=\frac{\frac{5}{4}+\frac{16}{3}-1}{\frac{1}{4}+\frac{3}{4}}$
$=\frac{15+64-12}{12\times \frac{4}{4}}$
$=\frac{67}{12}\left(Ans\right).$