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    Maths-
    General
    Easy

    Question

    if  2 tan space A plus c o t space A equals tan space B then c o t space A plus 2 tan space left parenthesis A minus B right parenthesis equals

    1. -1
    2. 0
      1. 1
    4. 1/2

    hintHint:

    In this question first we have to rearrange the expression by taking LCM and then use the formula tan open parentheses a minus b close parentheses equals fraction numerator tan open parentheses a close parentheses minus tan open parentheses b close parentheses over denominator 1 plus tan open parentheses a close parentheses tan open parentheses b close parentheses end fraction. After that we use tan open parentheses x close parentheses cot open parentheses x close parentheses equals 1.

    The correct answer is: 0

      In this question we are given 2 tan open parentheses A close parentheses plus cot open parentheses B close parentheses space equals tan open parentheses B close parentheses and we have to find the value of
      cot open parentheses A close parentheses plus 2 tan open parentheses A minus B close parentheses
      Step1: By using trigonometric formula.
      tan open parentheses a minus b close parentheses equals fraction numerator tan open parentheses a close parentheses minus tan open parentheses b close parentheses over denominator 1 plus tan open parentheses a close parentheses tan open parentheses b close parentheses end fraction
      => cot open parentheses A close parentheses plus 2 tan open parentheses A minus B close parentheses
      => cot open parentheses A close parentheses plus 2 open parentheses fraction numerator tan open parentheses A close parentheses minus tan open parentheses B close parentheses over denominator 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction close parentheses
      By taking LCM we get,
      =>fraction numerator cot open parentheses A close parentheses left parenthesis 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses right parenthesis plus 2 tan open parentheses A close parentheses minus 2 tan open parentheses B close parentheses over denominator 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction
      =>fraction numerator cot open parentheses A close parentheses plus cot open parentheses A close parentheses tan open parentheses A close parentheses tan open parentheses B close parentheses plus 2 tan open parentheses A close parentheses minus 2 tan open parentheses B close parentheses over denominator 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction
      We know that tan open parentheses x close parentheses cot open parentheses x close parentheses equals 1
      => fraction numerator cot open parentheses A close parentheses plus tan open parentheses B close parentheses plus 2 tan open parentheses A close parentheses minus 2 tan open parentheses B close parentheses over denominator 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction
      =>fraction numerator cot open parentheses A close parentheses plus 2 tan open parentheses A close parentheses minus tan open parentheses B close parentheses over denominator 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction
      We can write 2 tan open parentheses A close parentheses plus cot open parentheses B close parentheses space equals tan open parentheses B close parentheses
      => fraction numerator tan open parentheses B close parentheses minus tan open parentheses B close parentheses over denominator 1 plus tan open parentheses A close parentheses tan open parentheses B close parentheses end fraction
      =>0
      Hence the value of the expression cot open parentheses A close parentheses plus 2 tan open parentheses A minus B close parentheses is 0

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