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Definition of a Determinant

If α and β ar...

Question

If $α$ and $β$ are solutions of $s i n^{2} x$ + a sin x + b = 0 as well as that of $c o s^{2} x$ + c cos x + d = 0, then sin( $α$ + $β$ ) is equal to

A

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B

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C

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D

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Solution

The correct option is D

$\begin{matrix} s i n α + s i n β & = - a c o s α + c o s β & - c \end{matrix}}$ Applying transformation

sin ( $α$ + $β$ ) = $\frac{2 a c}{a^{2} + c^{2}}$

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