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Integration of Piecewise Continuous Functions

If α, β are...

Question

If $α, β$ are different values of $x$ satisfying
$a c o s x + b sin x = c$ , Then $t a n (\frac{α + β}{2}) =$

a + b

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a - b

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\frac{a}{b}

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\frac{b}{a}

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Solution

The correct option is C $\frac{b}{a}$
clearly $a cos α + b sin α = c = a cos β + b sin β$

$a (cos α - cos β) + b (sin α - sin β) = 0$

$a (2 sin \frac{α + β}{2} sin \frac{α - β}{2}) = b (2 cos \frac{α + β}{2} sin \frac{α - β}{2})$

$tan \frac{α + β}{2} = \frac{b}{a}$

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