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 \(\sin 2 \alpha=\)
- A \(\frac{-3}{5}\)
- B \(\frac{-24}{25}\)
- C \(\frac{-4}{25}\)
- D \(\frac{-13}{18}\)
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,…
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