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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\alpha\) is a root of the equation \(25 \cos ^2 \theta+5 \cos \theta-12=0\), for \(\frac{\pi}{2} < \alpha < \pi\), then \(\sin 2 \alpha=\)

  1. A \(\frac{-3}{5}\)
  2. B \(\frac{-24}{25}\)
  3. C \(\frac{-4}{25}\)
  4. D \(\frac{-13}{18}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{-24}{25}\)

Step-by-step Solution

Detailed explanation

Since, \(\alpha\) is a root of given equation, \(\begin{aligned} 25 \cos ^2 \theta+5 \cos \theta-12 & =0 \\ \frac{\pi}{2} & < \alpha < \pi\end{aligned}\) Then, \(\begin{aligned} D & =b^2-4 a c=(5)^2-4(25)(-12) \\ & =25+1200=1225\end{aligned}\) Now,…