Question

3tan3x=3 solve the equation for the exact solutions over the interval [0,2pi)

Answer 1

Six solutions are found by solving given trigonometric equation in the interval [0,2π).

We have to solve the equation, 3tan3x = 3 for the exact solutions over the interval [0,2π).

The equation is, 3tan3x = 3

⇒ tan3x = 3/3 = 1 = tan(π/4)

⇒ 3x = nπ + (π/4)

[ we know, tanx = tany than x = nπ + y ]

⇒x = nπ/3 + π/12

take, n = 0 , x = π/12

take, n = 1 , x = π/3

take, n = 2 , x = 3π/4

take, n = 3 , x = 13π/12

take, n = 4, x = 17π/12

take, n = 5, x = 21π/12

Therefore six solutions are found by solving given trigonometric equation in the interval [0,2π). these are ; π/12, π/3 , 3π/4 , 13π/12, 17π/12, 21π/12.

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