JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\tan A, \tan B\), where \(A, B \in \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)\), be the roots of the quadratic equation \(x^2 - 2x - 5 = 0\). Then \(20\sin^2\left(\dfrac{A+B}{2}\right)\) is equal to:
- A \(10 + \sqrt{10}\)
- B \(10 - 2\sqrt{10}\)
- C \(10 - 3\sqrt{10}\)
- D \(10 - \sqrt{10}\)
Answer & Solution
Correct Answer
(C) \(10 - 3\sqrt{10}\)
Step-by-step Solution
Detailed explanation
Given that \(\tan A\) and \(\tan B\) are the roots of the quadratic equation \(x^2 - 2x - 5 = 0\). Sum of the roots: \(\tan A + \tan B = 2\) Product of the roots: \(\tan A \tan B = -5\) Using the tangent addition formula:…
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