Question

Solve
$2({\cos }^2{45}^o+{\tan }^2{60}^o)-6({\sin }^2{45}^o-\tan {30}^o)$

Answer 1

$2({\cos }^{2}45°+{\tan }^{2}60°)-6({\sin }^{2}45°-\tan 30°)$

$=2({\left(\frac{1}{\sqrt{2}}\right)}^2+{\left(\sqrt{3}\right)}^2)-6({\left(\frac{1}{\sqrt{2}}\right)}^2-\frac{1}{\sqrt{3}})$

$=2(\frac{1}{2}+3)-6(\frac{1}{2}-\frac{1}{3})$

$=2\left(\frac{7}{2}\right)-6\left(\frac{1}{6}\right)$

$=7-1$

$=6$