What is the general solution of trigonometric equation $\sqrt{3} cot x + 1 = 0$ $sqrt3cotx+1=0$ ?

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Answer 1 · 2016-10-01T07:14:25

General solution of $\sqrt{3} cot x + 1 = 0$ $sqrt3cotx+1=0$ is $x = n π + \frac{2 π}{3}$ $x=npi+(2pi)/3$ , where $n$ $n$ is an integer.

As $\sqrt{3} cot x + 1 = 0$ $sqrt3cotx+1=0$ , we have

$\sqrt{3} cot x = - 1$ $sqrt3cotx=-1$

or $cot x = - \frac{1}{\sqrt{3}}$ $cotx=-1/sqrt3$

As $cot (\frac{π}{3}) = \frac{1}{\sqrt{3}}$ $cot(pi/3)=1/sqrt3$ and $cot (π - \frac{π}{3}) = \frac{1}{\sqrt{3}}$ $cot(pi-pi/3)=1/sqrt3$

i.e. $cot x = cot (\frac{2 π}{3})$ $cotx=cot((2pi)/3)$

Now as $cot$ $cot$ function has a cycle of $π$ $pi$ radians or $180^{o}$ $180^o$ , it repeats after every $π$ $pi$ radians or $180^{o}$ $180^o$ .

General solution of $\sqrt{3} cot x + 1 = 0$ $sqrt3cotx+1=0$ is $x = n π + \frac{2 π}{3}$ $x=npi+(2pi)/3$ , where $n$ $n$ is an integer.

What is the general solution of trigonometric equation sqrt3cotx+1=0√3cotx+1=0sqrt3cotx+1=0?