AP EAMCET · Maths · Quadratic Equation
If \(\tan \alpha\) and \(\tan \beta\) are the roots of the equation \(x^2+p x+q\) \(=0\), then the value of \(\sin ^2(\alpha+\beta)+p \cos (\alpha+\beta) \sin (\alpha\) \(+\beta)+q \cos ^2(\alpha+\beta)\) is
- A \(p+q\)
- B p
- C q
- D \(\frac{p}{p+q}\)
Answer & Solution
Correct Answer
(C) q
Step-by-step Solution
Detailed explanation
Given that, \(\tan \alpha\) and \(\tan \beta\) are the roots of the equation \(x^2+p x+q=0\) \[ \therefore \quad \tan \alpha+\tan \beta=-p \text { and } \tan \alpha \cdot \tan \beta=q \] Now, \(\quad \tan (\alpha+\beta)=\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta}\)…
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