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Inverse Trigonometric Functions

Question

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Find the value of the following :

$tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 7 space straight pi over denominator 6 end fraction close parentheses$

Solution

tan to the power of negative 1 end exponent open parentheses tan space fraction numerator 7 space straight pi over denominator 6 end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets tan open parentheses straight pi plus straight pi over 6 close parentheses close square brackets equals tan to the power of negative 1 end exponent open parentheses tan straight pi over 6 close parentheses equals straight pi over 6

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