44
Evaluate : $\frac{5}{\cot^2 30^\circ} + \frac{1}{\sin^2 60^\circ} - \cot^2 45^\circ + 2 \sin^2 90^\circ$
Show SolutionHide Solution↓
$$\begin{aligned}& \frac{5}{\cot^2 30^\circ} + \frac{1}{\sin^2 60^\circ} - \cot^2 45^\circ + 2 \sin^2 90^\circ \\ & = \frac{5}{(\sqrt{3})^2} + \frac{1}{(\sqrt{3}/2)^2} - (1)^2 + 2(1)^2 = \frac{5}{3} + \frac{4}{3} - 1 + 2 \\ & = \frac{9}{3} + 1 = 4 \\ & = 3 + 1 = 4 \\ & \text{OR}\end{aligned}$$