Question

tan 30° cosec 60° + tan 60° sec 30°

Answer 1

As we know that,
$$\begin{gathered} \tan 30°=\frac{1}{\sqrt{3}} \\ \sec 30°=\frac{2}{\sqrt{3}} \\ \mathrm{cosec}60°=\frac{2}{\sqrt{3}} \\ \tan 60°=\sqrt{3} \\ \mathrm{By}\mathrm{substituting}\mathrm{these}\mathrm{values},\mathrm{we}\mathrm{get} \\ \tan 30°\mathrm{cosec}60°+\tan 60°\sec 30°=\frac{1}{\sqrt{3}}\times \frac{2}{\sqrt{3}}+\sqrt{3}\times \frac{2}{\sqrt{3}} \\ =\frac{2}{3}+2 \\ =\frac{2+6}{3} \\ =\frac{8}{3} \\ \mathrm{Hence},\tan 30°\mathrm{cosec}60°+\tan 60°\sec 30°=\frac{8}{3} \end{gathered}$$