Mathematics

Mathematics

Problem

2. Choose the correct option and justify your choice : (i) 2tan⁡30∘1+tan⁡230∘=\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}= (A) sin⁡60∘\quad \sin 60^{\circ} (B) cos⁡60∘\cos 60^{\circ} (C) tan⁡60∘\tan 60^{\circ} (D) sin⁡30∘\sin 30^{\circ} (ii) 1−tan⁡245∘1+tan⁡245∘=\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}= (A) tan⁡90∘\quad \tan 90^{\circ} (B) 1 (C) sin⁡45∘\sin 45^{\circ} (D) 0 (iii) sin⁡2 A=2sin⁡ A\sin 2 \mathrm{~A}=2 \sin \mathrm{~A} is true when A=\mathrm{A}= (A) 0∘\quad 0^{\circ} (B) 30∘30^{\circ} (C) 45∘45^{\circ} (D) 60∘60^{\circ} (iv) 2tan⁡30∘1−tan⁡230∘=\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}= (A) cos⁡60∘\quad \cos 60^{\circ} (B) sin⁡60∘\sin 60^{\circ} (C) tan⁡60∘\tan 60^{\circ} (D) sin⁡30∘\sin 30^{\circ}

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