Question:medium

If \( \alpha = 3 + 4 + 8 + 9 + 13 + \dots \) up to 40 terms and \( (\tan \beta)^{\frac{\alpha}{1020}} \) is the root of the equation \( x^2 - x - 2 = 0 \), then the value of \( \sin^2 \beta + 3\cos^2 \beta \) is:

Updated On: Apr 9, 2026
  • 1
  • \(\frac{2}{3}\)
  • \(\frac{5}{3}\)
  • \(\frac{1}{3}\)
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The Correct Option is C

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