Question:medium

If both \( \alpha \) and \( \beta \) lie in \( \left(-\dfrac{\pi}{4},\,0\right] \), \( \sin(\alpha+\beta) = -\dfrac{33}{65} \), and \( \sin\alpha = -\dfrac{3}{5} \), then \( \tan(2\alpha+\beta) \) is

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When given \( \sin \theta \), always visualize the right-angled triangle (3-4-5 or 33-56-65) to find \( \cos \theta \) and \( \tan \theta \) quickly. Pay close attention to the quadrant to assign the correct signs.
Updated On: Jul 21, 2026
  • \( -\frac{9}{323} \)
  • \( -\frac{9}{125} \)
  • \( \frac{75}{323} \)
  • \( \frac{12}{5} \)
Show Solution

The Correct Option is D

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