Simplify the following expression completely and then find its numerical value:

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Simplify the following expression completely and then find its numerical value: (i) Simplify the numerator sin⁡(90∘−30∘) sec⁡30∘+cos⁡(90∘−30∘) csc⁡30∘\sin(90^{\circ}-30^{\circ})\,\sec30^{\circ}+\cos(90^{\circ}-30^{\circ})\,\csc30^{\circ}. (ii) Simplify the denominator tan⁡45∘+cot⁡45∘\tan45^{\circ}+\cot45^{\circ}. (iii) Hence, determine the value of the complete expression sin⁡(90∘−30∘) sec⁡30∘+cos⁡(90∘−30∘) csc⁡30∘tan⁡45∘+cot⁡45∘ .\frac{\sin(90^{\circ}-30^{\circ})\,\sec30^{\circ}+\cos(90^{\circ}-30^{\circ})\,\csc30^{\circ}}{\tan45^{\circ}+\cot45^{\circ}}\,.

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