Find the values of each of the expressions $tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 3 straight pi over denominator 4 end fraction close parentheses$ .

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Solution

tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 3 straight pi over denominator 4 end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets tan open parentheses straight pi minus straight pi over 4 close parentheses close square brackets equals tan to the power of negative 1 end exponent open parentheses negative tan straight pi over 4 close parentheses space space space space space space space space space space space space space space space space space space space space space equals tan to the power of negative 1 end exponent open square brackets tan space open parentheses negative straight pi over 4 close parentheses close square brackets equals negative straight pi over 4 space space space space space space space space space space space space space space space space space space space space open square brackets negative straight pi over 4 element of open parentheses negative straight pi over 2 comma straight pi over 2 close parentheses close square brackets

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