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

Let $a=\frac{5{\cos }^{2}60+4{\sec }^{2}30{\tan }^{2}45}{{\sin }^{2}30+{\cos }^{2}30}$

We know that, $\cos 60=\frac{1}{2}$

$\sec 30=\frac{2}{\sqrt{3}}$

$\tan 45=1$

${\sin }^2\theta +{\cos }^2\theta =1$

$a=\frac{5(\frac{1}{2}{)}^2+4(\frac{2}{\sqrt{3}})-1}{1}$

$a=\frac{5}{4}+\frac{16}{3}-1$

$a=\frac{5}{4}+\frac{13}{3}=\frac{57}{12}$