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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 $k π$ , then the value of k is

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Correct option is B

We have sinθ+2sinθ+3sinθ+4=6Since -1≤sinθ≤1, LHS≥6But RHS=6⇒sinθ=-1Since θ∈0,4π⇒θ=3π2,7π2∴sum of values of θ=3π2+7π2=5π=kπ ⇒k=5

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Let θ∈0,4π satisfy the equation sinθ+2sinθ+3sinθ+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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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 $k π$ , then the value of k is