Question

Evaluate the following: $2{\tan }^{2}45°·{\cos }^{2}30°·{\sin }^{2}60°$.

Answer 1

Given $2{\tan }^{2}45°·{\cos }^{2}30°·{\sin }^{2}60°$

To evaluate the given expression, substitute standard values of the trigonometric ratio as follows:

$\begin{array}{rcl}2{\tan }^{2}45°·{\cos }^{2}30°·{\sin }^{2}60°& =& 2·{\left(1\right)}^2·{\left(\frac{\sqrt{3}}{2}\right)}^2·{\left(\frac{\sqrt{3}}{2}\right)}^2\left[\because \tan 45°=1,\cos 30°=\frac{\sqrt{3}}{2},\sin 60°=\frac{\sqrt{3}}{2}\right]\\ & =& 2\times \frac{3}{4}\times \frac{3}{4}\\ & =& \frac{9}{8}\end{array}$

Hence, the required answer is $2{\tan }^{2}45°·{\cos }^{2}30°·{\sin }^{2}60°=\frac{9}{8}$.