If and ( ) are roots of the equation x^2 - 2 x + 3 - 2 2 = 0

MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If α\alpha and β\beta ( α>β\alpha > \beta ) are roots of the equation x2−2x+3−22=0, then the value ofx^2 - \sqrt{2}x + \sqrt{3 - 2\sqrt{2}} = 0, \text{ then the value of} (cos⁡−1α+tan⁡−1α+tan⁡−1β)(\cos^{-1} \alpha + \tan^{-1} \alpha + \tan^{-1} \beta) is equal to (1) 3π8\frac{3\pi}{8} (2) 5π8\frac{5\pi}{8} (3) 7π8\frac{7\pi}{8} (4) π3\frac{\pi}{3}

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