Pre-Calc Trig. Problem?

Question

If(2tanx/(1-tan^2x))=1, then x can equal?

Answer 1

(2tanx / (1 - tan²x)) = 1

Recall :Trigonometry formulas tan2A = (2tanA / (1 - tan²A))

Substitute (2tanx / (1 - tan²x)) = tan2x

Therefore tan2x = 1

Take arctan to each side

arctan(tan2x) = arctan(1)

Recall : trigonometry inverse function values  arctan(1) = π/4

arctantan(2x) = π/4

  Therefore 2x = π/4

Divide each side by 2

x = π/ 8.

 

Comments

tan(2x) = 1.

tan(2x) = tan(π/4).

General solution : If tan θ = tan ∝, then the general solution of θ = nπ + ∝, for n Є Z.

2x = nπ + π/4

⇒ x = (1/2)(nπ + π/4)

x = nπ/2 + π/8.

The general solution is x = nπ/2 + π/8 for n Є Z.