JAMB 1991 · UME · Q40

Simplify $\cos^2x(\sec^2x + \sec^2x\tan^2x)$ .

Worked solution (try it first)

Take out the common factor $\sec^2 x$ in the bracket: $\cos^2 x \sec^2 x(1 + \tan^2 x)$ .
$\cos^2 x \sec^2 x = 1$ , because $\sec x = \frac{1}{\cos x}$ .
That leaves $1 + \tan^2 x$ .
By the identity $1 + \tan^2 x = \sec^2 x$ , the answer is $\sec^2 x$ , option C.