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Some Applications Of Trigonometry

Question

Without using trigonometric tables, evaluate: $fraction numerator cos squared 20 degree plus cos squared 70 degree over denominator sin squared 59 degree plus sin squared 31 degree end fraction$
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Solution

fraction numerator cos left parenthesis 90 degree minus 70 degree right parenthesis plus cos squared 70 degree over denominator sin squared left parenthesis 90 degree minus 31 degree right parenthesis plus sin squared 31 degree end fraction equals fraction numerator sin squared 20 degree plus cos squared 70 degree over denominator cos squared 31 degree plus sin squared 31 degree end fraction space equals space 1