Question

Evaluate the following.
$\frac{5{\cos }^2{60}^o+4{\sec }^2{30}^o-{\tan }^2{45}^o}{{\sin }^2{30}^o+{\cos }^2{30}^o}$

Answer 1

$\frac{5{\cos }^2{60}^o+4{\sec }^2{30}^o-{\tan }^2{45}^o}{{\sin }^2{30}^o+{\cos }^2{30}^o}=\frac{5\ast \frac{1}{4}+4\ast \frac{4}{3}-1}{\frac{1}{4}+\frac{3}{4}}=\frac{\frac{5}{4}+\frac{16}{3}-1}{1}=\frac{79}{12}-1=\frac{67}{12}$