Write the value of $open parentheses 2 tan to the power of negative 1 end exponent 1 fifth close parentheses$

Solution

We know:
$2 tan to the power of negative 1 end exponent straight x space equals space tan to the power of negative 1 end exponent fraction numerator 2 straight x over denominator 1 minus straight x squared end fraction rightwards double arrow space 2 tan to the power of negative 1 end exponent 1 fifth space equals space tan to the power of negative 1 end exponent fraction numerator 2 open parentheses begin display style 1 fifth end style close parentheses over denominator 1 minus open parentheses begin display style 1 fifth end style close parentheses squared end fraction space equals space tan to the power of negative 1 end exponent fraction numerator begin display style 2 over 5 end style over denominator begin display style 24 over 25 end style end fraction equals tan to the power of negative 1 end exponent 5 over 12 therefore space space tan open parentheses 2 tan to the power of negative 1 end exponent 1 fifth close parentheses space equals space tan open parentheses tan to the power of negative 1 end exponent 5 over 12 close parentheses equals 5 over 12$

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Inverse Trigonometric Functions

Write the value of $open parentheses 2 tan to the power of negative 1 end exponent 1 fifth close parentheses$

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