JAMB 1986 · UME · Q32

If $\cos\theta = \dfrac ab$ , find $1 + \tan^2\theta$ .

Worked solution (try it first)

Use the identity $1 + \tan^2\theta = \sec^2\theta$ .
$\sec\theta = \dfrac{1}{\cos\theta}$
$= \dfrac ba$ , so $\sec^2\theta = \dfrac{b^2}{a^2}$ , option A.