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Question

If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by 6 0 to the power of 0 end exponent, then c o s blank B equals

  1. 1    
  2. fraction numerator square root of 13 minus 1 over denominator 4 end fraction    
  3. fraction numerator 1 over denominator 2 end fraction    
  4. fraction numerator 1 minus square root of 13 over denominator 4 end fraction    

The correct answer is: fraction numerator square root of 13 minus 1 over denominator 4 end fraction


    a comma b comma c are in GP
    equals succeeds b to the power of 2 end exponent equals a c equals succeeds s i n to the power of 2 end exponent B equals blank s i n blankA s i n blank C
    equals 2 s i n to the power of 2 end exponent B equals blank c o s blank left parenthesis A minus C right parenthesis minus blank c o s blank left parenthesis A plus C right parenthesis
    equals 2 left parenthesis 1 minus c o s to the power of 2 end exponent B right parenthesis equals blank c o s blank 6 0 to the power of 0 end exponent minus blank c o s blank left parenthesis 18 0 to the power of 0 end exponent minus B right parenthesis

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