If $s i n^{3} x - 2 s i n^{2} x - (K + 1) s i n x + 2 - K = 0$ ; $s i n x \neq - 1$ posses a solution for finite integral values of K only, then the number of positive integral value of K are equal to

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Solution

The correct option is B 5
$(s i n^{2} x - 3 s i n x + 2) (s i n x + 1) = K (s i n x + 1)$
$K = {(s i n x - \frac{3}{2})}^{2} - \frac{1}{4}$
$K ϵ [0, 6); (K \neq 6 ∵ s i n x \neq= - 1)$
$K = {1, 2, 3, 4, 5}$

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