Simplify the expression and state its numerical value.

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Simplify the expression 3sin⁡12∘cos⁡18∘+3cos⁡12∘sin⁡18∘−2(cos⁡45∘cos⁡15∘−sin⁡45∘sin⁡15∘)3\sin 12^{\circ}\cos 18^{\circ}+3\cos 12^{\circ}\sin 18^{\circ}-2\bigl(\cos 45^{\circ}\cos 15^{\circ}-\sin 45^{\circ}\sin 15^{\circ}\bigr) and state its numerical value.

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