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    Maths-
    General
    Easy

    Question

    The expression fraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction can be written as

    1. sin space A cos space A plus 1
    2. s e c space A cos space e c A plus 1
    3. tan space A plus c o t space A
    4. s e c space A plus cos e c space A

    hintHint:

    We have been given an expressionfraction numerator tan space A over denominator 1 minus cat space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space d end fraction and we are required to find the simpler version of the expression.

    The correct answer is: s e c space A cos space e c A plus 1

      Step by step solution:
      Given, fraction numerator tan space A over denominator 1 minus c o t space A end fraction plus fraction numerator cot space A over denominator 1 minus tan space A end fraction
      equals fraction numerator begin display style tan A end style over denominator 1 minus begin display style fraction numerator 1 over denominator tan A end fraction end style end fractionplus fraction numerator begin display style fraction numerator 1 over denominator tan A end fraction end style over denominator 1 minus begin display style tan A end style end fractionequals fraction numerator begin display style tan A end style over denominator begin display style fraction numerator tan A minus 1 over denominator tan A end fraction end style end fractionplus fraction numerator begin display style 1 end style over denominator begin display style tan A left parenthesis 1 minus tan A right parenthesis end style end fraction
      equals space fraction numerator tan squared A over denominator tan A minus 1 end fractionnegative fraction numerator 1 over denominator tan A left parenthesis tan A minus 1 right parenthesis end fractionequals fraction numerator tan cubed A minus 1 over denominator tan A left parenthesis tan A minus 1 right parenthesis end fraction
      equals space fraction numerator left parenthesis tan A minus 1 right parenthesis over denominator tan A left parenthesis tan A minus 1 right parenthesis end fractionleft parenthesis tan squared A plus tan A plus 1 right parenthesis
      equals fraction numerator begin display style fraction numerator sin squared A over denominator cos squared A end fraction end style plus begin display style fraction numerator sin A over denominator cos A end fraction end style plus 1 over denominator begin display style fraction numerator sin A over denominator cos A end fraction end style end fractionequals fraction numerator sin squared A plus sin A cos A plus cos squared A over denominator sin A cos A end fraction
      equals fraction numerator 1 plus sin A cos A over denominator sin A cos A end fractionequals s e c A cos e c A plus 1
      Hence, option(c) is the correct option.

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