JAMB 2013 · UTME · Q34

If $\tan\theta = \frac34$ , find the value of $\sin\theta + \cos\theta$ .

Worked solution (try it first)

$\tan\theta = \frac34$ , so draw a right-angled triangle with opposite side 3 and adjacent side 4.
Pythagoras gives the hypotenuse $\sqrt{9 + 16} = 5$ .
So $\sin\theta = \frac35$ and $\cos\theta = \frac45$ .
Add: $\frac35 + \frac45 = \frac75 = 1\frac25$ , option D.