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Let $θ \in [0, 4 π]$ satisfy the equation $(\sin θ + 2) (\sin θ + 3) (\sin θ + 4) = 6$ . If the sum of all the values of $θ$ is of the form $kπ,$ then the value of k is

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answer is B.

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Detailed Solution

$(\sin θ + 2) (\sin θ + 3) (\sin θ + 4) = 6$

$L.H.S. \geq 6 and R.H.S. = 6$

Therefore, equality only holds if

$\begin{array}{l} \sin θ = - 1 or θ = 3 π / 2, 7 π / 2 \\ ∴ Sum = 5 π \Rightarrow k = 5 \end{array}$

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