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  • The principal value of the given equation  <img alt="\mathrm{y=cosec^{-1}\frac{2}{\sqrt{3}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%3Dcosec%5E%7B-1%7D%5C

The principal value of the given equation  \mathrm{y=cosec^{-1}\frac{2}{\sqrt{3}}} is

Option: 1

\frac{\pi}{6}


Option: 2

\frac{\pi}{3}


Option: 3

\frac{\pi}{2}


Option: 4

\frac{\pi}{4}


Answers (1)

best_answer

 Option (b) \frac{\pi}{3}

Given that,

\mathrm{ y=cosec^{-1}\frac{2}{\sqrt{3}}}

\mathrm{ cosec\ y=\left (\frac{2}{\sqrt{3}} \right)}

We know that the range of the principal value branch of \mathrm{cosec^{-1}x\: is\: \left ( -\frac{\pi}{2},\frac{\pi}{2} \right )-\left \{ 0 \right \}.}

Thus,

\mathrm{cosec\left ( \frac{\pi}{3} \right )=\frac{2}{\sqrt{3}}

Therefore, the principal value of \mathrm{cosec^{-1}\frac{2}{\sqrt{3}}=\frac{\pi}{3}. }

 

Posted by

Ritika Harsh

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