Question

Evaluate:
${\tan }^2{30}^o\sin {30}^o+\cos {60}^o{\sin }^2{90}^o{\tan }^2{60}^o-2\tan {45}^o{\cos }^2{0}^o\sin {90}^o$

Answer 1

${\tan }^{2}30\sin 30+\cos 60{\sin }^{2}90{\tan }^{2}60-2\tan 45{\cos }^{2}0\sin 90$

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

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

$=\frac{1+9-12}{6}$

$=\frac{-2}{6}$

$=\frac{-1}{3}$