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Inverse Trigonometric Functions

Question

Wired Faculty App

Find the principal values of the following

$tan to the power of negative 1 end exponent left parenthesis negative square root of 3 right parenthesis$

Solution

Let space straight y space equals space tan to the power of negative 1 end exponent left parenthesis negative square root of 3 right parenthesis space space space space space space space space space where space minus straight pi over 2 less than straight y less than straight pi over 2 therefore space space space tan space y space equals space minus square root of 3 space space space space space space space space space space space space where space minus straight pi over 2 space less than straight y less than straight pi over 2 therefore space space space tan space straight y space equals space minus tan straight pi over 3 equals tan open parentheses negative straight pi over 3 close parentheses space where space minus straight pi over 2 less than straight y less than straight pi over 2 therefore space space space space straight y equals negative straight pi over 3

therefore

required principal value =

negative straight pi over 3

.

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