Find value :-  1/3(cos^2 30 -  sin^2 45) + 2(sin^4 60- sec^4 45) +2/3 tan^2 60 
  1. 65/24
  2. 4/3
  3. 24/65

Asked by sucharitasahoo1 | 26th Dec, 2017, 05:59: PM

Expert Answer:

begin mathsize 16px style 1 third open parentheses cos squared 30 minus sin squared 45 close parentheses plus 2 open parentheses sin to the power of 4 60 minus sec to the power of 4 45 close parentheses plus 2 over 3 tan squared 60
equals fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction open square brackets open parentheses fraction numerator begin display style square root of 3 end style over denominator 2 end fraction close parentheses squared minus open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared close square brackets plus 2 open parentheses open parentheses fraction numerator begin display style square root of 3 end style over denominator 2 end fraction close parentheses to the power of 4 minus open parentheses square root of 2 close parentheses to the power of 4 close parentheses plus fraction numerator begin display style 2 end style over denominator begin display style 3 end style end fraction cross times open parentheses square root of 3 close parentheses squared
equals fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction open square brackets fraction numerator begin display style 3 end style over denominator 4 end fraction minus 1 half close square brackets plus 2 open parentheses fraction numerator begin display style 9 end style over denominator 16 end fraction minus 4 close parentheses plus fraction numerator begin display style 2 end style over denominator begin display style 3 end style end fraction cross times 3
equals 1 third cross times 1 fourth plus 2 cross times open parentheses fraction numerator negative 55 over denominator 16 end fraction close parentheses plus 2
equals 1 over 12 minus 55 over 8 plus 2
equals fraction numerator 2 minus 165 over denominator 24 end fraction plus 2
equals fraction numerator negative 163 over denominator 24 end fraction plus 2
equals fraction numerator negative 115 over denominator 24 end fraction


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Answered by Sneha shidid | 27th Dec, 2017, 12:01: PM