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Question

If 2 tan to the power of negative 1 end exponent invisible function application left parenthesis cos invisible function application x right parenthesis equals tan to the power of negative 1 end exponent invisible function application left parenthesis 2 text cosec  end text x right parenthesis comma then x =

  1. fraction numerator 3 pi over denominator 4 end fraction    
  2. fraction numerator pi over denominator 4 end fraction    
  3. fraction numerator pi over denominator 3 end fraction    
  4. None of these    

The correct answer is: fraction numerator pi over denominator 4 end fraction


    We have 2tan to the power of negative 1 end exponent invisible function application left parenthesis cos invisible function application x right parenthesis equals tan to the power of negative 1 end exponent invisible function application left parenthesis 2 text cosec end text x right parenthesis
    Þ tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 2 cos invisible function application x over denominator 1 minus cos to the power of 2 end exponent invisible function application x end fraction close parentheses= tan to the power of negative 1 end exponent invisible function application left parenthesis 2 text cosec  end text x right parenthesis
    fraction numerator 2 cos invisible function application x over denominator sin to the power of 2 end exponent invisible function application x end fraction equals 2 text cosec end text x rightwards double arrow 2 cos invisible function application x equals 2 sin invisible function application x
    or sin invisible function application x equals cos invisible function application x
    rightwards double arrow x equals fraction numerator pi over denominator 4 end fraction.

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