Q

Find the principal and general solutions of the following equations cot x = - (3)^(1/2)

Find the principal and general solutions of the following equations:

Q (3)   $\small \cot x = - \sqrt{3}$

Views

we know that    $\ cot\frac{\pi}{6} = \sqrt{3}$   and we know that $\ \cot\frac{5\pi}{6} = \cot\left ( \pi -\frac{\pi}{6} \right ) = -cot\frac{\pi}{6} = -\sqrt{3}$

Similarly , the value for $\ \cot\frac{11\pi}{6} = \cot\left ( 2\pi -\frac{\pi}{6} \right ) = -cot\frac{\pi}{6} = -\sqrt{3}$
Therefore, principal solution is x = $\frac{5\pi}{6} \ and \ \frac{11\pi}{6}$

We also  know that the value of cot x repeats after an interval of $\pi$
There the general solution is x  = $n\pi \pm \frac{5\pi}{6} \ where \ n \ \epsilon \ Z$

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