JAMB 1985 · UME · Q34

Without using tables, calculate the value of $1 + \sec^2 30^\circ$ .

Worked solution (try it first)

$\sec30^\circ = \dfrac{1}{\cos30^\circ}$
$= \dfrac{1}{\sqrt3/2}$
$= \dfrac{2}{\sqrt3}$ .
Square it: $\sec^2 30^\circ = \dfrac{4}{3}$ .
Add 1: $1 + \frac43 = \frac73 = 2\frac13$ , option A.