If \( f(\theta)=\tan \left(\sin ^{-1} \sqrt{\frac{2}{3+\cos 2 \thet...

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If \( f(\theta)=\tan \left(\sin ^{-1} \sqrt{\frac{2}{3+\cos 2 \theta}}\right) \), then
\( \mathrm{P} \)
(1) \( f\left(\frac{\pi}{4}\right)=1 \)
(2) \( f\left(\frac{\pi}{4}\right)=\sqrt{2} \)
(3) \( \frac{d(f(\theta))}{d(\cos \theta)} \) at \( \theta=\frac{\pi}{4} \) is -2
(4) \( f^{\prime}\left(\frac{\pi}{4}\right)=\sqrt{2} \)
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