Question : If $5\cos\theta+12\sin\theta=13,\ 0^0<\theta<90^0$, then the value of $\sin\theta$ is:
Option 1: $\frac{5}{13}$
Option 2: $–\frac{12}{13}$
Option 3: $\frac{6}{13}$
Option 4: $\frac{12}{13}$
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Correct Answer: $\frac{12}{13}$
Solution :
Given: $5\cos\theta+12\sin\theta=13,\ 0^0<\theta<90^0$
Here, $5\cos\theta+12\sin\theta=13$
⇒ $(\frac{5}{13})\cos\theta+(\frac{12}{13})\sin\theta=1$
Comparing it with $\cos^2\theta+\sin^2\theta=1$ we get,
$\cos\theta=\frac{5}{13}$ and $\sin\theta=\frac{12}{13}$
Hence, the correct answer is $\frac{12}{13}$.
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