TS EAMCET · Maths · Trigonometric Equations
\(\alpha, \beta\) are the roots of the equation \(\sin ^2 x+b \sin x+c=0\). If \(\alpha+\beta=\frac{\pi}{2}\) then \(b^2-1=\)
- A \(c\)
- B \(2c\)
- C \(c^2\)
- D \(4 c^2\)
Answer & Solution
Correct Answer
(B) \(2c\)
Step-by-step Solution
Detailed explanation
\(\sin \alpha + \sin \beta = -b\) \(\sin \alpha \sin \beta = c\) Given \(\alpha+\beta=\frac{\pi}{2}\), so \(\sin \beta = \sin(\frac{\pi}{2}-\alpha) = \cos \alpha\). \(\sin \alpha + \cos \alpha = -b\) \(\sin \alpha \cos \alpha = c\)…
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