Question

tan^2 30+ tan^2 45 + tan^2 60 − 13/3

Answer 1

$\text{Given: \( \tan ^{2} 30^{\circ}+\tan ^{2} 45^{\circ}+\tan ^{2} 30^{\circ} \)}$

Solution:

$\rm \tan ^{2} 30^{\circ}+\tan ^{2} 45^{\circ}+\tan ^{2} 60^{\circ}$

$\[ \begin{array}{l}\displaystyle \rm =\left(\frac{1}{\sqrt{3}}\right)^{2}+(1)^{2}+(\sqrt{3})^{2} \\\\ \displaystyle \rm =\frac{1}{3}+1+3 \\\\ \displaystyle \rm =\frac{1+3+9}{3} \\\\ \boxed{\red{ \displaystyle \rm =\frac{13}{3}}} \end{array} \]$