Mathematics

Mathematics

Problem

## EXERCISE 8.2 1. Evaluate the following: (i) sin⁡60∘cos⁡30∘+sin⁡30∘cos⁡60∘\sin 60^{\circ} \cos 30^{\circ}+\sin 30^{\circ} \cos 60^{\circ} (ii) 2tan⁡245∘+cos⁡230∘−sin⁡260∘2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ} (iii) cos⁡45∘sec⁡30∘+cosec⁡30∘\frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}} (iv) sin⁡30∘+tan⁡45∘−cosec⁡60∘sec⁡30∘+cos⁡60∘+cot⁡45∘\frac{\sin 30^{\circ}+\tan 45^{\circ}-\operatorname{cosec} 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}} (v) 5cos⁡260∘+4sec⁡230∘−tan⁡245∘sin⁡230∘+cos⁡230∘\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}

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