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value of  \sec^{-1}\sec(\frac{5\pi}{4}) ?

Option: 1

\frac{3\pi}{4}


Option: 2

\frac{5\pi}{4}


Option: 3

\frac{\pi}{4}


Option: 4

-\frac{3\pi}{4}


Answers (1)

best_answer

Graph of sec-1( sec (x))

 

\\\frac{5\pi}{4} \text{does not in the range of }[0,\pi] \\ \frac{5\pi}{4} \in [\pi,2\pi], \text{and from graph value of y for this branch equals } 2\pi-x \\\\So,\sec^{-1}\sec(\frac{5\pi}{4})= 2\pi-\frac{5\pi}{4}= \frac{3\pi}{4}

 

Alternate solution (Non-Graphical)

\\\frac{5\pi}{4} \text{does not in the range of }[0,\pi] \\ \sec^{-1}\sec(\frac{5\pi}{4})=\sec^{-1}\sec(2\pi-\frac{3\pi}{4})\\=\sec^{-1}\sec(\frac{3\pi}{4}) \\=\frac{3\pi}{4}\\\\(Since, \frac{3\pi}{4} \,\,lies\,\,in\,\,[0,\pi])

Posted by

Devendra Khairwa

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