Question : What is the value of $\frac{3 \operatorname{cosec} 42°}{\sec 48°}-\frac{5 \cos 32°}{\sin 58°}$?
Option 1: - 1
Option 2: 5
Option 3: 0
Option 4: - 2
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Correct Answer: - 2
Solution :
Given, $\frac{3 \operatorname{cosec} 42°}{\sec 48°}-\frac{5 \cos 32°}{\sin 58°}$
We know, $\operatorname{cosec}\theta = \frac{1}{\sin\theta}$, $\cos(90°-\theta)= \sin\theta$, and $\sec\theta = \frac{1}{cos\theta}$
$\therefore$ Given equation becomes,
$\frac{3\cos48°}{\sin 42°}-\frac{5\cos32°}{\sin58°}$
= $\frac{3\cos(90°-42°)}{\sin42°}-\frac{5\cos(90°-58°)}{\sin58°}$
= $\frac{3\sin42°}{\sin 42°}-\frac{5\sin58°}{\sin 58°}$
= 3 - 5
= - 2
Hence, the correct answer is - 2.
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