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If $D = |\begin{array}{ccc} 1 & \cos θ & 1 \\ - \sin θ & 1 & - \cos θ \\ - 1 & \sin θ & 1 \end{array}|$ then D lies in the interval

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Correct option is C

Expanding D, we get D=1+sin⁡θcos⁡θ−cos⁡θ(−sin⁡θ−cos⁡θ)+−sin2⁡θ+1=2+sin⁡2θ+cos⁡2θ=2+2cos⁡(2θ−π/4)As −1≤cos⁡(2θ−π/4)≤1,2−2≤D≤2+2

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If D=1cos⁡θ1−sin⁡θ1−cos⁡θ−1sin⁡θ1 then D lies in the interval

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If $D = |\begin{array}{ccc} 1 & \cos θ & 1 \\ - \sin θ & 1 & - \cos θ \\ - 1 & \sin θ & 1 \end{array}|$ then D lies in the interval