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AP EAMCET · Maths · Quadratic Equation

If \(\sin \alpha=p\), then the quadratic equation whose roots are \(\tan \frac{\alpha}{2}, \cot \frac{\alpha}{2}\) is

  1. A \(p x^2-2 x+p=0\)
  2. B \(p x^2+2 x+p=0\)
  3. C \(p x^2+x+p=0\)
  4. D \(p x^2-x+p=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(p x^2-2 x+p=0\)

Step-by-step Solution

Detailed explanation

Since, \(\sin \alpha=p \Rightarrow \frac{2 \tan \frac{\alpha}{2}}{1+\tan ^2 \frac{\alpha}{2}}=p\) ...(i) and sum of roots \(=\tan \frac{\alpha}{2}+\cot \frac{\alpha}{2}\) \(=\frac{\tan ^2 \frac{\alpha}{2}+1}{\tan \frac{\alpha}{2}}=\frac{2}{p}\) [from Eq. (i)] and product of…