Question

find the principal and general solutions of the following equations. 1) cosec x= -2​

Answer 1

Given ,

The equation is Cosec(x) = -2

Thus ,

Sin(x) = -1/2

Sin(x) = - Sin(π/6)

Sin(x) = Sin(-π/6)

We know that , if sin(x) = sin(y) , then

$\boxed{ \sf{x = n\pi + {( - 1)}^{n} y}}$

Thus ,

The general solution will be

$\sf x = n\pi + {( - 1)}^{n} ( - \frac{\pi}{6} )$

And the principal solution :

$\sf x = - \frac{\pi}{6} \: , \: \frac{7\pi}{6} \: .....$