Pre Calculus Question

Question

2tanx/1-tan^2x = 1/square root of 3; what are the values of x

Answer 1

2tanx/1-tan^2x = 1/sqr3

literally means

2tanx -tan2(x) = (sqr3)/3

graph left side and graph right side, see the x values where the lines intersect:

x= about .34, 1.03, 3.48, 4.17, ...

x=about 0.34 +.69n or 1.03+.69n radians where n = any integer

the problem is ambiguous

if you interpret it differently, see the other posted solutions

Answer 2

tan(A + B) = [tanA + tanB] / [1 - tanAtanB]

So, if A = B = x, your equation is equivalent to tan(2x) = 1 / √3

Solve for x.

Answer 3

2x = tan¹(1/√3)

2x = π/6 + kπ, k any integer

x = π/12 + kπ/2, k any integer

x = π/12 + 6kπ/12 , k any int

x = (6k+1)π/12

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