The expression $3 \cos \theta + 5 \sin \theta$ is defined for \(0 \le \theta \le \frac{\pi}{2

Question

The expression $3 \cos \theta + 5 \sin \theta$ is defined for $0 \le \theta \le \frac{\pi}{2}$ radians. Express $3 \cos \theta + 5 \sin \theta$ in the form $R \cos(\theta - \alpha)$, where $R > 0$ and $\alpha$ is an acute angle in radian.[2] Hence, solve the equation $3 \cos \theta + 5 \sin \theta = 4$,[2] find the minimum value of $\frac{1}{(3 \cos \theta + 5 \sin \theta)^2 + 1}$.[2]

Accepted Answer

$1-\frac{1}{x-3}+\frac{3}{x+1}+\frac{3}{(x+1)^2}$

2025 SST PRELIMS P1 Q6

2025 SST PRELIMS P1 Q6

Solution:

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