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$If A = [\begin{array}{ccc} 1 + \cos^{2} θ & \sin^{2} θ & 4 \cos 6 θ \\ \cos^{2} θ & 1 + \sin^{2} θ & 4 \cos 6 θ \\ \cos^{2} θ & \sin^{2} θ & 1 + 4 \cos 6 θ \end{array}] is a singular matrix and 3 θ \in (0, π) then θ =$

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a

π9

b

π18

c

π6

d

π12

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detailed solution

Correct option is A

|A|=0⇒2+4cos⁡6θ=0⇒cos⁡6θ=−12 ⇒6θ=2π3⇒θ=π9

Similar Questions

If [ ] denotes the greatest integer less than or equal to the real number under consideration, and $- 1 \leq x < 0, 0 \leq y < 1$ , $1 \leq z < 2$ , then the value of the determinant $|\begin{array}{ccc} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{array}|$ is

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