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Inverse Trigonometric Functions

Question

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Find the value of the following :

$cos to the power of negative 1 end exponent open parentheses cos space fraction numerator 13 straight pi over denominator 6 end fraction close parentheses$

Solution

cos to the power of negative 1 end exponent open parentheses cos space fraction numerator 13 straight pi over denominator 6 end fraction close parentheses equals cos to the power of negative 1 end exponent open square brackets cos open parentheses 2 straight pi plus straight pi over 6 close parentheses close square brackets equals cos to the power of negative 1 end exponent open parentheses cos space straight pi over 6 close parentheses equals straight pi over 6

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