Find the solutions of the equation that are in the interval [0, π/2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

Question

Find the solutions of the equation that are in the interval [0, π/2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

tan 6x = tan 3x

x=

Answer 1

tan 6x = tan 3x

tan (2(3x)) = tan 3x

(2 tan 3x) / (1 - tan² 3x) = tan 3x

2 / (1 - tan² 3x) = 1

2 = 1 - tan² 3x

1 = -tan² 3x

-1 = tan² 3x

∅

Answer 2

Let z = 3x to get tan2z = tanz

2tanz / (1 - tan²z) = tanz

2tanz = tanz - tan³z

tan³z + tanz = 0

tanz (tan²z + 1) = 0

tanz = 0

z = 0 , π , 2π , ...

3x = 0 , π , 2π , ...

x = 0 , π / 3 , ... (those are the only 2 solutions in the given interval)

Answer 3

ZER0

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