How do you solve this trigonometric equation?
Solve the equation for solutions in the interval $[0,2 \pi)$. $$\left(\cot(x) -1 \right) \left( 2 \sin(x) + \sqrt{3} \right) = 0.$$
How do you solve this trigonometric equation?
Solve the equation for solutions in the interval $[0,2 \pi)$. $$\left(\cot(x) -1 \right) \left( 2 \sin(x) + \sqrt{3} \right) = 0.$$
A product of two real valued quantities is zero if and only if one of the terms in the product is zero.
So, here, either $$ \cot x-1=0 $$ or $$ 2\sin x +\sqrt 3=0. $$ Equivalently either $\cot x=1$ or $\sin x =-\sqrt 3/2$. Can you find the solutions to these? Remember to only take solutions in $[0,2\pi)$.