The solution to the trigonometric equation is x = π/3, π/2, 2π/3, π option first is correct.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a trigonometric equation shown in the picture.
[tex]\rm 2\sin \left(x\right)\tan \left(2x\right)-\sqrt{3}\tan \left(2x\right)=0[/tex]
[tex]\rm \tan \left(2x\right)\left(2\sin \left(x\right)-\sqrt{3}\right)=0[/tex]
tan2x = 0
[tex]\rm x=\dfrac{\pi n}{2}[/tex]
Plug n = 0, 1, 2
x = 0, π/2, π
or
[tex]\rm 2\sin \left(x\right)-\sqrt{3}=0[/tex]
[tex]\rm \:x=\dfrac{\pi }{3}+2\pi n \ \ \ \ or \ \ \ x=\dfrac{2\pi }{3}+2\pi n[/tex]
Plug n = 0
x = π/3, 2π/3
The solutions are:
x = π/3, π/2, 2π/3, π
Thus, the solution to the trigonometric equation is x = π/3, π/2, 2π/3, π option first is correct.
Learn more about trigonometry here:
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