Some Applications of Trigonometry

Without using trigonometric tables, evaluate. - Wired Faculty

Question

Without using trigonometric tables, evaluate.
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Solution

fraction numerator cos space 58 degree over denominator sin space 32 degree end fraction plus fraction numerator sin space 22 degree over denominator cos space 68 degree end fraction minus fraction numerator cos space 38 degree. space cosec space 52 degree over denominator tan space 18 degree. space tan space 35 degree. space tan 60 degree. space tan 72 degree. space tan 55 degree end fraction

equals space fraction numerator cos space left parenthesis 90 degree space minus 32 degree right parenthesis over denominator sin space 32 degree end fraction plus fraction numerator sin space 22 degree over denominator cos space left parenthesis 90 degree minus 22 degree right parenthesis end fraction minus fraction numerator cos space 38 degree. space cosec space left parenthesis 90 degree minus 38 degree right parenthesis over denominator tan space 18 degree. space tan space 35 degree. space left parenthesis square root of 3 right parenthesis. space tan space left parenthesis 90 degree minus 18 degree right parenthesis. space tan space left parenthesis 90 degree minus 35 degree right parenthesis end fraction space

space equals space fraction numerator sin space 32 degree over denominator sin space 32 degree end fraction plus fraction numerator sin space 22 degree over denominator sin space 22 degree end fraction minus fraction numerator cos space 38 degree. space sec space 38 degree over denominator square root of 3 left parenthesis tan space 18 degree. space tan space 35 degree. space cot space 18 degree. space cot space 35 degree right parenthesis end fraction

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