Published by:
CGP EDU Academic Team
Published on: September 12, 2026
If 
, then find the value of 
.
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: Given the equation \( \alpha = \sec(3\beta) \).
Step 2: Differentiate both sides with respect to \( \beta \):
\( \frac{d\alpha}{d\beta} = \frac{d}{d\beta}[\sec(3\beta)]
= \sec(3\beta) \tan(3\beta) \cdot (3)
= 3 \sec(3\beta) \tan(3\beta)
Therefore, \( \frac{d\alpha}{d\beta} = 3 \sec(3\beta) \tan(3\beta) \) is the required value.
Step 2: Differentiate both sides with respect to \( \beta \):
\( \frac{d\alpha}{d\beta} = \frac{d}{d\beta}[\sec(3\beta)]
= \sec(3\beta) \tan(3\beta) \cdot (3)
= 3 \sec(3\beta) \tan(3\beta)
Therefore, \( \frac{d\alpha}{d\beta} = 3 \sec(3\beta) \tan(3\beta) \) is the required value.
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