Some Applications of Trigonometry

Question

Without using the trigonometric tables, evaluate the following:
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Solution

11 over 7 fraction numerator sin left parenthesis 90 degree minus 20 degree right parenthesis over denominator cos space 20 degree end fraction minus 4 over 7 fraction numerator cos left parenthesis 90 degree minus 37 degree right parenthesis space cross times space cosec space 37 degree over denominator tan left parenthesis 90 degree minus 75 degree right parenthesis space cross times space tan space 75 degree cross times tan left parenthesis 90 degree minus 55 degree right parenthesis cross times tan space 55 degree end fraction

equals space 11 over 7 minus 4 over 7 space equals space 7 over 7 space equals space 1