NECO 2022 · Paper 1 · Q43

Given that $\sin\theta = \frac{3}{5}$ where $\theta$ is an acute angle, what is the value of $\dfrac{\sin\theta + \cos\theta}{1 - \tan\theta}$ ?

Worked solution (try it first)

Use a 3–4–5 right triangle: $\cos\theta = \frac{4}{5}$ and $\tan\theta = \frac{3}{4}$ .
The top is $\frac{3}{5} + \frac{4}{5} = \frac{7}{5}$ and the bottom is $1 - \frac{3}{4} = \frac{1}{4}$ .
Dividing by $\frac{1}{4}$ multiplies by 4: $\frac{28}{5} = 5\frac{3}{5}$ , option D.