Find the general solution of cosecx=-2

Asked by Pragya Singh | 1 year ago |  66

##### 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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