Find the general solution of cosecx=-2

Asked by Pragya Singh | 1 year ago |  66

1 Answer

Solution :-

Here it is given that,

cosecx=-2

Now we know that

\(cosec \dfrac{\pi}{6}=2\)

 \( cosec (π +\dfrac{\pi}{6})= cosec \dfrac{\pi}{6}a\)

= -2

And,

\( cosec (2π -\dfrac{\pi}{6})= -cosec \dfrac{\pi}{6}\) = -2

therefore we have,

\( cosec \dfrac{7\pi}{6}=-2\) and \( cosec \dfrac{11\pi}{6}=-2\)

Hence , the principal solutions are

\(x= \dfrac{7\pi}{6}\) and \( \dfrac{11\pi}{6}\)

cosec =\( \dfrac{1}{sinx}\)

And we know,

Therefore , we have,

\(sin x=sin \dfrac{7\pi}{6}\)

Which implies,

\( x=n\pi +(-1)^n \dfrac{7\pi}{6}\;n\in Z\)

Answered by Abhisek | 1 year ago

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