Question

Evaluate each of the following

$ta{n}^2{30}^o+ta{n}^2{60}^o+ta{n}^2{45}^o$

Answer 1

tan${30}^{\circ }$ = $\frac{1}{\sqrt{3}}$

tan ${60}^{\circ }$ = $\sqrt{3}$

tan ${45}^{\circ }$ = 1

$ta{n}^2{30}^o+ta{n}^2{60}^o+ta{n}^2{45}^o$

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

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

= $\frac{13}{4}$