If f(θ)=∣1tan⁡θ1−tan⁡θ1tan⁡θ−1−tan⁡θ1∣f(\theta) = \begin{vmatrix} 1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1 \end{vmatrix}…

Mathematics

Problem

If f(θ)=∣1tan⁡θ1−tan⁡θ1tan⁡θ−1−tan⁡θ1∣f(\theta) = \begin{vmatrix} 1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1 \end{vmatrix} , then the set f(θ):0≤θ<π2f(\theta) : 0 \le \theta < \frac{\pi}{2} is a. (−∞,−1)∪(1,∞)(-\infty, -1) \cup (1, \infty) b. [2,∞)[2, \infty) c. (−∞,0]∪[2,∞)(-\infty, 0] \cup [2, \infty) d. (−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty)

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