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If $f(θ) =\begin{vmatrix}1&\tan θ&1\\-\tan θ&1&\tan θ\\-1&-\tan θ&1\end{vmatrix}$, then the set $\{f(θ):0≤θ≤\frac{π}{2}\}$ is |
$(-∞, 0]∪[2,∞)$ $[2,∞)$ $(-∞, 0)∪(0,∞)$ $(-∞, -1]∪[1,∞)$ |
$[2,∞)$ |
Applying $R_1 → R_1 + R_3$, we get $f(θ) =\begin{vmatrix}θ&0&2\\-\tan θ&1&\tan θ\\-1&-\tan θ&1\end{vmatrix}$ $=2 (\tan^2θ+1)=2 \sec^2 θ>2$ $∴f(θ) ∈[2,∞)$. |
