Question

Evaluate:
$3{\cos }^2{30}^{\circ }+{\sec }^2{30}^{\circ }+2\cos 0^{\circ }+3sin{90}^{\circ }-{\tan }^2{60}^{\circ }$

Answer 1

We have,
$3co{s}^2{30}^{\circ }+se{c}^2{30}^{\circ }+2cos{0}^{\circ }+3sin{90}^{\circ }-ta{n}^2{60}^{\circ }$

$=3(cos{30}^{\circ }{)}^2+(sec{30}^{\circ }{)}^2+2cos{0}^{\circ }+3sin{90}^{\circ }-(tan{60}^{\circ }{)}^2$

$=3\times {\left(\frac{\sqrt{3}}{2}\right)}^2+{\left(\frac{2}{\sqrt{3}}\right)}^2+2\times 1+3\times 1-(\sqrt{3}{)}^2=\frac{9}{4}+\frac{4}{3}+2+3-3=\frac{67}{12}$