Question

Evaluate : $\frac{4}{{cot}^2{30}^0}+\frac{1}{{sin}^2{30}^{0.}}-2{cos}^2{45}^0-{sin}^2{0}^0$

Answer 1

$\frac{4}{{\cot }^2{30}^{\circ }}+\frac{1}{{\sin }^2{30}^{\circ }}-2{\cos }^2{45}^{\circ }-{\sin }^2{0}^{\circ }$

$=\frac{4}{{\left(\sqrt{3}\right)}^2}+\frac{1}{{\left(\frac{1}{2}\right)}^2}-2{\left(\frac{1}{\sqrt{2}}\right)}^2-0$

$=\frac{4}{3}+4-2\times \frac{1}{2}$

$=\frac{4}{3}+4-1$

$=\frac{4}{3}+3$

$=\frac{4+9}{3}=\frac{13}{3}$