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त्रिकोणमिति का परिचय

Question
CBSEHHIMAH10010462

निम्नलिखित के मान ज्ञात कीजिए। 
fraction numerator sin space 30 degree space plus space tan space 45 degree space minus space cosec space 60 degree over denominator sec space 30 degree space plus cos space 60 degree space plus space cot space 45 degree end fraction

Solution
fraction numerator sin space 30 degree space plus space tan space 45 degree space minus space cosec space 60 degree over denominator sec space 30 degree space plus cos space 60 degree space plus space cot space 45 degree end fraction
equals space fraction numerator begin display style 1 half end style plus 1 minus begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style plus begin display style 1 half end style plus 1 end fraction space equals space fraction numerator begin display style 3 over 2 end style minus begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style plus begin display style 3 over 2 end style end fraction space equals space fraction numerator begin display style fraction numerator 3 square root of 3 minus 4 over denominator 2 square root of 3 end fraction end style over denominator begin display style fraction numerator 4 plus 3 square root of 3 over denominator 2 square root of 3 end fraction end style end fraction
equals space fraction numerator 3 square root of 3 minus 4 over denominator 4 plus 3 square root of 3 end fraction space equals space fraction numerator left parenthesis 3 square root of 3 minus 4 right parenthesis thin space left parenthesis 3 square root of 3 minus 4 right parenthesis over denominator left parenthesis 4 plus 3 square root of 3 right parenthesis thin space left parenthesis 3 square root of 3 minus 4 right parenthesis end fraction
equals space fraction numerator 27 minus 2 cross times 3 square root of 3 cross times 4 plus 16 over denominator 27 minus 16 end fraction space equals fraction numerator 43 minus 24 square root of 3 over denominator 11 end fraction

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