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  • The principal value of the given equation   <img alt="y=cos^{-1}\left ( \frac{1}{\sqrt{2}} \right )" src="https://entrancecorner.oncodecogs.com/gif.latex?y%3Dcos%5E%7B-1%7D%5Cleft%20

The principal value of the given equation   y=cos^{-1}\left ( \frac{1}{\sqrt{2}} \right )   is

 

Option: 1

\frac{\pi}{4}


Option: 2

\frac{\pi}{3}


Option: 3

\frac{\pi}{2}


Option: 4

\frac{\pi}{6}


Answers (1)

best_answer

Given that,

y=cos^{-1}\left ( \frac{1}{\sqrt{2}} \right )

 cos\ y=\left ( \frac{1}{\sqrt{2}} \right )

We know that the range of the principal value branch of  cos^{-1}x \: \: is \left ( 0,\pi \right ).

Thus,

cos\left ( \frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}

Therefore, the principal value of   cos^{-1}\left ( \frac{1}{\sqrt{2}} \right )=\frac{\pi}{4}.

 

Posted by

Sanket Gandhi

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