If \( \int \frac{\sin \theta-\cos \theta}{(\sin \theta+\cos \theta) \sqrt{\sin \theta \cos \thet....

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If \( \int \frac{\sin \theta-\cos \theta}{(\sin \theta+\cos \theta) \sqrt{\sin \theta \cos \theta+\sin ^{2} \theta \cos ^{2} \theta}} d \theta= \) \( \operatorname{cosec}^{-1}(f(\theta))+C \), then
(1) \( f(\theta)=\sin 2 \theta+1 \)
(2) \( f(\theta)=1-\sin 2 \theta \)
(3) \( f(\theta)=\sin 2 \theta-1 \)
(4) none of these
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