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Question

Find real part of cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator i over denominator 2 end fraction close parentheses

  1. pi divided by 3    
  2. pi divided by 4    
  3. logopen parentheses fraction numerator square root of 3 minus 1 over denominator 2 end fraction close parentheses    
  4. None of these    

The correct answer is: pi divided by 4


    because Expression cos to the power of negative 1 end exponent invisible function application left parenthesis cos invisible function application theta plus i sin invisible function application theta right parenthesis
    equals sin to the power of negative 1 end exponent invisible function application square root of sin invisible function application theta end root minus i log invisible function application left parenthesis square root of sin invisible function application theta end root plus square root of 1 plus sin invisible function application theta end root right parenthesis, where theta equals fraction numerator pi over denominator 6 end fraction
    thereforeReal part of cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator i over denominator 2 end fraction close parentheses equals sin to the power of negative 1 end exponent invisible function application square root of fraction numerator 1 over denominator 2 end fraction end root= fraction numerator pi over denominator 4 end fraction.

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