Which of the following when simplified does not reduce to unity ?

Mathematics · JEE Main · NTA Exams — Trigonometry

1. \[\frac{1-2 \sin ^{2} \alpha}{2 \cot \left(\frac{\pi}{4}+\alpha\right) \cos ^{2}\left(\frac{\pi}{4}-\alpha\right)}\]
2. \[\frac{\sin (\pi-\alpha)}{\sin \alpha-\cos \alpha \tan \frac{\alpha}{2}}+\cos (\pi-\alpha)\]
3. \[\frac{1}{4 \sin ^{2} \alpha \cos ^{2} \alpha}-\frac{\left(1-\tan ^{2} \alpha\right)^{2}}{4 \tan ^{2} \alpha}\]
4. \(\frac{1+\sin 2 \alpha}{2(\sin \alpha+\cos \alpha)^{2}}\)

Answer

(D) 1+ 2 2( + )^ 2

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