WAEC 2023 · Paper 1 · Q31

Find the value of $\alpha$ in the equation $\cos(\alpha + 14)^\circ = \sin(4\alpha + 6)^\circ$ .

Worked solution (try it first)

The cosine of an angle equals the sine of its complement, so the two angles add up to $90^\circ$ : $(\alpha + 14) + (4\alpha + 6) = 90$ .
Collect terms: $5\alpha + 20 = 90$ , so $5\alpha = 70$ .
Divide by 5: $\alpha = 14$ , option A.
(Check: the angles are $28^\circ$ and $62^\circ$ .)