Mathematics

Mathematics

Problem

Evaluate the following expressions, giving each answer in simplest form. a. (i) A=sin⁡30∘ cos⁡60∘+cos⁡45∘ sin⁡60∘A=\sin 30^{\circ}\,\cos 60^{\circ}+\cos 45^{\circ}\,\sin 60^{\circ}. b. (ii) B=sin⁡60∘cos⁡30∘+cos⁡60∘sin⁡30∘B=\dfrac{\sin 60^{\circ}}{\cos 30^{\circ}}+\dfrac{\cos 60^{\circ}}{\sin 30^{\circ}}. c. (iii) Hence find C=A×BC=A\times B.

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