Evaluate:
$fraction numerator sec left parenthesis 90 degree minus straight theta right parenthesis times cosecθ space minus space tan left parenthesis 90 degree minus straight theta right parenthesis space cotθ plus left parenthesis cos squared 35 degree plus cos squared 55 degree right parenthesis over denominator tan 5 degree space tan space 15 degree space tan space 45 degree space tan space 75 degree space tan space 85 degree end fraction.$

Solution

fraction numerator cosecθ. space cosecθ space minus space cotθ. cotθ plus open square brackets cos squared left parenthesis 90 degree minus 55 degree right parenthesis plus cos squared 55 degree close square brackets over denominator tan 5 degree. space tan 85 degree space tan 15 degree space tan space 75 degree space tan space 45 degree end fraction

fraction numerator cosec squared straight theta minus cot squared straight theta plus open square brackets sin squared 55 degree plus cos squared 55 degree close square brackets over denominator tan space left parenthesis 90 degree minus 85 degree right parenthesis. space tan space 85 degree space tan left parenthesis 90 degree minus space 75 degree right parenthesis space tan space 75 degree end fraction

fraction numerator 1 plus 1 over denominator cot space 85 degree. space tan 85 degree space tan left parenthesis 90 degree minus 75 degree right parenthesis space tan space 75 degree end fraction

fraction numerator 2 over denominator 1.1 end fraction space equals space 2 over 1 space equals space 2.

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