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Analytic Trigonometry

+1 vote
Please explain steps.

Find all solutions to the equation.

tan3x+1=sec3x
asked Feb 14, 2013 in TRIGONOMETRY by payton Apprentice

1 Answer

+1 vote

tan(3x) + 1 = sec(3x)

Apply square each side.

[tan(3x) + 1]2 = [sec(3x)]2

tan2(3x)+ 1 + 2tan(3x) = sec2(3x)

Pythagorean Identities: tan2θ+1 = sec2θ

sec2(3x) + 2tan(3x) = sec2(3x)

Subtract sec2(3x) from each side.

2tan(3x) = 0

Divide each side by 2.

tan(3x) = 0

3x = arc tan(0) = 0, 2π, 4π..............

Divide each side by 3.

x = 0, 2π/3, 4π/3, ..............

Therefore x = 0, 2π/3, 4π/3, ..............

answered Feb 15, 2013 by britally Apprentice

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