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निम्नलिखित के मान ज्ञात कीजिए। - Wired Faculty

Question

निम्नलिखित के मान ज्ञात कीजिए।
$fraction numerator 5 cos squared 60 degree plus 4 sec squared 30 degree minus tan squared 45 degree over denominator sin squared 30 degree plus cos squared 30 degree end fraction$

Solution

fraction numerator 5 cos squared 60 degree plus 4 sec squared 30 degree minus tan squared 45 degree over denominator sin squared 30 degree plus cos squared 30 degree end fraction

equals space fraction numerator 5 open parentheses begin display style 1 half end style close parentheses squared plus 4 open parentheses begin display style fraction numerator 2 over denominator square root of 3 end fraction end style close parentheses squared minus left parenthesis 1 right parenthesis squared over denominator open parentheses begin display style 1 half end style close parentheses squared plus open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses squared end fraction space equals space fraction numerator 5 begin display style 1 fourth end style plus 4 cross times begin display style 4 over 3 end style minus 1 over denominator begin display style 1 third end style plus begin display style 3 over 4 end style end fraction equals space fraction numerator begin display style 1 over 12 end style left parenthesis 15 plus 64 minus 12 right parenthesis over denominator begin display style fraction numerator 1 plus 3 over denominator 4 end fraction end style end fraction space equals space fraction numerator begin display style 1 half end style cross times 67 over denominator begin display style 4 over 4 end style end fraction space equals space 67 over 12