Let θ∈[0,4π] satisies the equation (cosθ+1)(cosθ+2)(cosθ+3)=24, then the sum of all the values of θ is of the form kπ then K =

Let $θ \in [0, 4 π]$ satisies the equation $(\cos θ + 1) (\cos θ + 2) (\cos θ + 3) = 24$ , then the sum of all the values of $θ$ is of the form $k π$ then K =

A
B
C
D

Solution:

$T h e m a x i m u m v a l u e o f \cos θ i s 1$

We have $L H S \leq 24, R H S = 24$

$∴ L H S = R H S = 24$

$\Rightarrow \cos θ = 1 \Rightarrow θ = 0, 2 π, 4 π$

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