TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\tan \theta\) and \(\cot \theta\) are two distinct roots of the equation \(a x^2+b x+c=0, a \neq 0, b \neq 0\), then
- A \(\cos 2 \theta=-\frac{2 b}{c}\)
- B \(\sin 2 \theta=-\frac{2 c}{b}\)
- C \(\tan 2 \theta=\frac{2 b}{c}\)
- D \(\cot 2 \theta=\frac{2 c}{a}\)
Answer & Solution
Correct Answer
(B) \(\sin 2 \theta=-\frac{2 c}{b}\)
Step-by-step Solution
Detailed explanation
\(\tan \theta \cdot \cot \theta = \frac{c}{a} \Rightarrow 1 = \frac{c}{a} \Rightarrow c=a\) \(\tan \theta + \cot \theta = -\frac{b}{a}\) \(\frac{1}{\sin \theta \cos \theta} = -\frac{b}{a}\) \(\frac{2}{\sin 2\theta} = -\frac{b}{a}\) \(\frac{2}{\sin 2\theta} = -\frac{b}{c}\)…
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