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15 tan^3x=5tanx,(0,2pi)

Sagot :

Answer:

steps below

Step-by-step explanation:

15 tan³x=5tanx     .... (0,2π)

5tanx(3tan²x - 1) = 0

tanx = 0            x = π  (0° is excluded)

or 3tan²x - 1 = 0

(√3 tanx + 1) (√3 tanx - 1) = 0

tanx = 1 /√3      x = π/6 (30°)    or    x = 5π/6  (150°)

tanx = - 1 /√3      x = 7π/6 (210°)    or    x = 11π/6  (330°)

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