Show that $\frac{\tan x}{1 + \sec x} + \frac{1 + \sec x}{\tan x} = \frac{2}{\sin x}$.[5] Henc

Question

Show that $\frac{\tan x}{1 + \sec x} + \frac{1 + \sec x}{\tan x} = \frac{2}{\sin x}$.[5] Hence solve the equation $\frac{\tan x}{1 + \sec x} + \frac{1 + \sec x}{\tan x} = 1 + 3\sin x$ for $0^{\circ} \le x \le 360^{\circ}$.[4]

Accepted Answer

(ii) $x=41.8^\circ$ or $138.2^\circ$, to $1$ decimal place; $x=270^\circ$ is rejected because the original expression is undefined.

2024 FMSS PRELIMS P1 Q10

2024 FMSS PRELIMS P1 Q10

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