Some Applications of Trigonometry

Evaluate without using trigonometric tables: - Wired Faculty

Question

Evaluate without using trigonometric tables:
$fraction numerator 3 space cos space 55 degree over denominator 7 space sin space 35 degree end fraction minus fraction numerator 4 left parenthesis cos space 70 degree. space cosec space 20 degree right parenthesis over denominator 7 left parenthesis tan space 5 degree. space tan space 25 degree. space tan space 45 degree. space space tan space 65 degree. space tan space 85 degree right parenthesis end fraction.$

Solution

fraction numerator 3 space cos space 55 degree over denominator 7 space sin space space 35 degree end fraction

space minus space fraction numerator 4 left parenthesis cos space 70 degree. space cosec space 20 degree right parenthesis over denominator 7 left parenthesis tan space 5 degree. space tan space 25 degree. space tan space 45 degree. space tan space 65 degree. space tan space 85 degree right parenthesis end fraction

fraction numerator 3 space cos space left parenthesis 90 degree space minus 35 degree right parenthesis over denominator 7 space sin space 35 degree end fraction minus fraction numerator 4 left square bracket cos space left parenthesis 90 degree minus 20 degree right parenthesis. space cosec space 20 degree right square bracket over denominator 7 left square bracket tan space left parenthesis 90 degree minus 85 degree right parenthesis. space tan space 85 degree. space tan space left parenthesis 90 degree minus 65 degree right parenthesis. space tan space 65 degree. space tan space 45 degree end fraction.

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