Question

2. Write the principal solutions of cosec x = -2/√3.

Answer 1

Step-by-step explanation:

We have,

$\cosec(x) = - \frac{2}{ \sqrt{3} }$

$\implies \sin(x) = - \frac{ \sqrt{3} }{2}$

$\implies \sin(x) = \sin( - \frac{\pi}{3} )$

$\implies \: x = n\pi - ( - 1)^{n}. \frac{\pi}{3}$

For principal solutions, put n = 1 and 2

So,

Principal solutions are

$x = \pi + \frac{\pi}{3} \: \: and \: \: 2\pi - \frac{\pi}{3}$

$\implies \: x = \frac{4\pi}{3} \: \: and \: \: \frac{5\pi}{3}$