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Inverse Trigonometric Functions

Question

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Find the principal values of the following

$sec to the power of negative 1 end exponent open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses$

Solution

Let space straight y space equals sec to the power of negative 1 end exponent open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses space space space space where space space straight y element of open square brackets 0 comma straight pi over 2 close square brackets union open square brackets straight pi over 2 comma straight pi close square brackets therefore space space space space space sec space straight y equals fraction numerator 2 over denominator square root of 3 end fraction space space space where space space straight y element of open square brackets 0 comma straight pi over 2 close square brackets union open square brackets straight pi over 2 comma straight pi close square brackets therefore space space space straight y equals straight pi over 3

therefore

required principal value =

straight pi over 3

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