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Inverse Trigonometric Functions

Question

Wired Faculty App

Find the principal values of the following

$cos e c to the power of negative 1 end exponent left parenthesis negative square root of 2 right parenthesis$

Solution

Let space straight y space equals cosec to the power of negative 1 end exponent left parenthesis negative square root of 2 right parenthesis space space space where space straight y element of space open square brackets negative straight pi over 2 comma space 0 close square brackets union open square brackets 0 comma straight pi over 2 close square brackets therefore space space space space space cosec space straight y space equals space minus square root of 2 space space space space space where space space open square brackets negative straight pi over 2 comma space 0 close square brackets union open square brackets 0 comma straight pi over 2 close square brackets therefore space space space space space space cosec space straight y space equals space minus space cosec space straight pi over 4 equals space cosec space open parentheses negative straight pi over 4 close parentheses space space space where space space open square brackets negative straight pi over 2 comma space 0 close square brackets union open square brackets 0 comma straight pi over 2 close square brackets therefore space space space space space space straight y space equals space minus straight pi over 4

therefore

required principal value =

negative straight pi over 4

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