Question

(tan 30° cosec 60° + tan 60° sec 30°) = ?
(a) $2\frac{1}{3}$
(b) $2\frac{2}{3}$
(c) $3\frac{1}{3}$
(d) $1\frac{2}{3}$

Answer 1

(b ) $2\frac{2}{3}$

$$\begin{gathered} \left(\tan {30}^{\mathrm{o}}\mathrm{cosec}{60}^{\mathrm{o}}+\tan {60}^{\mathrm{o}}\sec {30}^{\mathrm{o}}\right) \\ =\left(\frac{1}{\sqrt{3}}\times \frac{2}{\sqrt{3}}+\sqrt{3}\times \frac{2}{\sqrt{3}}\right) \\ =\left(\frac{2}{3}+2\right)=2\frac{2}{3} \end{gathered}$$