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    Maths-
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    Question

    increment A B C comma if sin to the power of 2 end exponent invisible function application fraction numerator A over denominator 2 end fraction comma sin to the power of 2 end exponent invisible function application fraction numerator B over denominator 2 end fraction and sin to the power of 2 end exponent invisible function application fraction numerator C over denominator 2 end fraction are in H.P., thenblank a comma blank b blankandblank c blankwill be in

    1. A.P.  
    2. G.P.  
    3. H.P.  
    4. None of these  

    The correct answer is: H.P.

      fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator A over denominator 2 end fraction end fraction comma fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator B over denominator 2 end fraction end fraction comma fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator C over denominator 2 end fraction end fraction blank a r e blank i n blank A. P.
      rightwards double arrow fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator C over denominator 2 end fraction end fraction minus fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator B over denominator 2 end fraction end fraction equals fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator B over denominator 2 end fraction end fraction minus fraction numerator 1 over denominator sin to the power of 2 end exponent invisible function application fraction numerator A over denominator 2 end fraction end fraction
      rightwards double arrow fraction numerator a b over denominator open parentheses s minus a close parentheses open parentheses s minus b close parentheses end fraction minus fraction numerator a c over denominator open parentheses s minus a close parentheses open parentheses s minus c close parentheses end fraction equals fraction numerator a c over denominator open parentheses s minus a close parentheses open parentheses s minus c close parentheses end fraction minus fraction numerator b c over denominator open parentheses s minus b close parentheses open parentheses s minus c close parentheses end fraction
      rightwards double arrow open parentheses fraction numerator a over denominator s minus a end fraction close parentheses open parentheses fraction numerator b open parentheses s minus c close parentheses minus c open parentheses s minus b close parentheses over denominator open parentheses s minus b close parentheses open parentheses s minus c close parentheses end fraction close parentheses equals open parentheses fraction numerator c over denominator s minus c end fraction close parentheses open parentheses fraction numerator a open parentheses s minus b close parentheses minus b open parentheses s minus a close parentheses over denominator open parentheses s minus a close parentheses open parentheses s minus b close parentheses end fraction close parentheses
      rightwards double arrow a b minus a c equals a c minus b c
      rightwards double arrow a b plus b c equals 2 a c
      rightwards double arrow fraction numerator 1 over denominator c end fraction plus fraction numerator 1 over denominator a end fraction equals fraction numerator 2 over denominator b end fraction comma blank i. e. comma blank a comma blank b comma blank c blankare in H.P.

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