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Standard X

Mathematics

Quadratic Formula

If tan A, t...

Question

If $tan A, tan B$ are the roots of the quadratic $a b x^{2} - c^{2} x + a b = 0$ , where $a, b, c$ are the sides of a triangle, then prove
$cos C = 0$

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Solution

$a b x^{2} - c^{2} x + a b = 0$
$α = tan A, β = tan B$
$α + β = tan A + tan B = \frac{c^{2}}{a b}$
$tan A tan B = \frac{a b}{a b} = 1$
$tan (A + B) = \frac{tan A + tan B}{1 - tan A tan B}$
$tan (A + B) = \frac{\frac{c^{2}}{a b}}{1 - 1}$
$tan (A + B) = \infty$
$A + B = \frac{π}{2}$
Given, $A + B + C = π$
$C = \frac{π}{2}$
$cos C = 0$

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If tanA,tanB are the roots of the quadratic ab x2−c2x+ab=0, where a,b,c are the sides of a triangle, then provecosC=0

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