9514 1404 393
Answer:
nπ -π/6 . . . for any integer n
Explanation:
tan(x) +√3 = -2tan(x) . . . . . given
3tan(x) = -√3 . . . . . . . . . . . add 2tan(x)-√3
tan(x) = -√3/3 . . . . . . . . . . divide by 3
x = arctan(-√3/3) = -π/6 . . . . use the inverse tangent function to find x
This is the value in the range (-π/2, π/2). The tangent function repeats with period π, so the set of values of x that will satisfy this equation is ...
x = n·π -π/6 . . . . for any integer n