Answer:
Step-by-step explanation:
Start by moving the 3 to the other side of the equals sign to get
[tex]tan^2(2\theta)=3[/tex]
[tex]tan^2(2\theta)=(tan(2\theta))(tan(2\theta))[/tex] so with that replacement:
[tex](tan(2\theta))(tan(2\theta))=3[/tex]
By the Zero Product Property,
[tex]tan(2\theta)=3[/tex] or [tex]tan(2\theta)=3[/tex]
Yes these are both the same, so we only need one of them. Once we find the angle, they are both the same, so we only need one of these equations.
If
[tex]tan(2\theta)=3[/tex], take the inverse tangent of both sides to give you:
[tex]2\theta=tan^{-1}(3)[/tex] and
[tex]2\theta=71.565[/tex] so
[tex]\theta=35.8[/tex]
Tangent increases in increments of pi or 180, so the other angle within the given interval is 35.8 + 180 = 215.8
