Question : If $\sec(7\theta+28°)= \operatorname{cosec} (30°-3\theta)$. Then, the value of $\theta$ is:
Option 1: 8°
Option 2: 5°
Option 3: 60°
Option 4: 9°
Answer (1)
25th Jan, 2024
Correct Answer: 8°
Solution :
Given: If $\sec(7\theta+28°)= \operatorname{cosec} (30°–3\theta)$.
$\sec A = \operatorname{cosec} B$, when $A+B = 90°$
Then, $7\theta +28° + 30°-3 \theta = 90°$
⇒ $4\theta + 58° = 90°$
⇒ $4\theta = 90°-58°$
⇒ $4\theta = 32°$
$\therefore \theta = \frac{32°}{4} = 8°$
Hence, the correct answer is 8°.
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