Find the principal and general solutions of the following equations:

Q (3)   \small \cot x = - \sqrt{3}

Answers (1)

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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