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निम्नलिखित के मान लिखिए: - Wired Faculty

Question

निम्नलिखित के मान लिखिए:
$fraction numerator cos space 45 degree over denominator sec space 30 degree space plus space cosec space 30 degree end fraction$

Solution

fraction numerator cos space 45 degree over denominator sec space 30 degree plus cosec space 30 degree end fraction

open square brackets because space cos space 45 degree space equals space fraction numerator 1 over denominator square root of 2 end fraction comma space sec space 30 degree space equals space fraction numerator 2 over denominator square root of 3 end fraction comma space cosec space 30 degree space equals 2 close square brackets

equals space fraction numerator begin display style fraction numerator 1 over denominator square root of 2 end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction plus 2 over 1 end style end fraction space equals space fraction numerator begin display style fraction numerator 1 over denominator square root of 2 end fraction end style over denominator begin display style fraction numerator 2 plus 2 square root of 3 over denominator square root of 3 end fraction end style end fraction

equals space fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 3 over denominator 2 plus 2 square root of 3 end fraction equals space fraction numerator square root of 3 over denominator square root of 2 left parenthesis 2 plus 2 square root of 3 right parenthesis end fraction equals space fraction numerator square root of 3 over denominator 2 square root of 2 plus 2 square root of 6 end fraction cross times fraction numerator 2 square root of 2 minus 2 square root of 6 over denominator 2 square root of 2 minus 2 square root of 6 end fraction equals space fraction numerator square root of 3 left parenthesis 2 square root of 2 minus 2 square root of 6 right parenthesis over denominator left parenthesis 2 square root of 2 right parenthesis squared minus left parenthesis 2 square root of 6 right parenthesis squared end fraction

equals space fraction numerator 2 square root of 6 minus 2 square root of 18 over denominator 8 minus 24 end fraction equals fraction numerator 2 square root of 6 minus 6 square root of 2 over denominator negative 16 end fraction equals space fraction numerator 2 left parenthesis square root of 6 minus 3 square root of 2 right parenthesis over denominator negative 16 end fraction equals fraction numerator 3 square root of 2 minus square root of 6 over denominator 8 end fraction