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AM,GM,HM Inequality

Sin A and Sin...

Question

Sin A and Sin B are the roots of the equation $c x^{2} - c (a + b) x + a b = 0$ . Then Sin C $=$

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\frac{1}{2}

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\frac{1}{\sqrt{2}}

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Solution

The correct option is D 1
$sin A + sin B = \frac{a + b}{c}$ ....eq(i)

$\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c} = k$

$sin A = k a, sin B = k b, sin C = k c$ .....substitute the values of a,b,c in eq(i)

$s i n A + s i n B = \frac{\frac{sin A}{k} + \frac{sin B}{k}}{\frac{sin c}{k}}$

$sin c = 1$ .

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