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Statement-I: integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator 1 over denominator square root of 5 end fraction t a n x over 2 right parenthesis plus c
Statement-II: If a>b then integral subscript blank superscript blank fraction numerator d x over denominator a plus b c o s x end fraction equals fraction numerator 2 over denominator square root of a squared minus b squared end root end fraction t a n to the power of negative 1 end exponent left parenthesis square root of fraction numerator a minus b over denominator a plus b end fraction end root t a n x over 2 right parenthesis plus c

  1. Statement I is true, statement II true, statement II is the correct explanation for statement II    
  2. Statement I is true, statement II true, statement II is not the correct explanation for statement II    
  3. Statement I is true, statement II is false    
  4. Statement I is false, statement II is true    

The correct answer is: Statement I is true, statement II true, statement II is the correct explanation for statement II


    Put tan x fraction numerator x over denominator 2 end fraction equals t d x equals fraction numerator 2 d r over denominator 1 plus C to the power of 2 end exponent end fraction comma c o s x equals fraction numerator 1 minus r to the power of 2 end exponent over denominator 1 plus C to the power of 2 end exponent end fraction
    not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 c o s x end fraction d x not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 3 plus 2 left parenthesis fraction numerator 1 minus t to the power of 2 end exponent over denominator 1 plus t to the power of 2 end exponent end fraction right parenthesis end fraction. fraction numerator 2 d r over denominator 1 plus C to the power of 2 end exponent end fraction equals 2 not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator 5 plus C to the power of 2 end exponent end fraction d t
    equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator r over denominator square root of 5 end fraction right parenthesis plus c
    equals fraction numerator 2 over denominator square root of 5 end fraction t a n to the power of negative 1 end exponent left parenthesis fraction numerator t a n fraction numerator x over denominator 2 end fraction over denominator square root of 5 end fraction right parenthesis plus C

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