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प्रश्न
Find the maximum value of \[\begin{vmatrix}1 & 1 & 1 \\ 1 & 1 + \sin \theta & 1 \\ 1 & 1 & 1 + \cos \theta\end{vmatrix}\]
उत्तर
Let Δ = \[\begin{vmatrix}1 & 1 & 1 \\ 1 & 1 + \sin \theta & 1 \\ 1 & 1 & 1 + \cos \theta\end{vmatrix}\]
Applying
\[= \sin\theta\cos\theta\]
\[ = \frac{\sin2\theta}{2}\]
We know that −1 ≤ sin2θ ≤ 1.∴ Maximum value of ∆ = \[\frac{1}{2} \times 1 = \frac{1}{2}\]
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