Without using trigonometric tables

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Without using trigonometric tables, evaluate each of the following. Show all steps clearly. (a) sin⁡(90∘−30∘)+cos⁡30∘\sin(90^{\circ}-30^{\circ})+\cos30^{\circ} (b) tan⁡60∘×cot⁡(90∘−60∘)\tan60^{\circ}\times\cot(90^{\circ}-60^{\circ}) (c) sec⁡30∘−csc⁡(90∘−30∘)\sec30^{\circ}-\csc(90^{\circ}-30^{\circ}) (d) csc⁡(90∘−45∘)×sin⁡45∘\csc(90^{\circ}-45^{\circ})\times\sin45^{\circ}

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