If \( \int_{0}^{\pi / 3} \frac{\tan \theta}{\sqrt{2 k \sec \theta}}...

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If \( \int_{0}^{\pi / 3} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(k0) \), then the value of \( k \) is (2019 Main, 9 Jan II)
P
(a) 1
(b) \( \frac{1}{2} \)
(c) 2
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