What is the general solution for tan(3x)=tan(pix) ?

The general solution for tan(3x)=tan(pix) is x=(2pin)/(3-pi),x= pi/(3-pi)+(2pin)/(3-pi)

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tan(3x)=tan(pix)

tan (3 x) = tan (π x)

x = \frac{2 πn}{3 - π}, x = \frac{π}{3 - π} + \frac{2 πn}{3 - π}

Solution steps

tan (3 x) = tan (π x)

Subtract

tan (π x)

from both sides

tan (3 x) - tan (π x) = 0

Express with sin, cos

\frac{- cos ( 3 x ) sin ( x π ) + cos ( x π ) sin ( 3 x )}{cos ( 3 x ) cos ( x π )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (3 x) sin (x π) + cos (x π) sin (3 x) = 0

Rewrite using trig identities

sin (3 x - x π) = 0

General solutions for

sin (3 x - x π) = 0

3 x - x π = 0 + 2 πn, 3 x - x π = π + 2 πn

Solve

3 x - x π = 0 + 2 πn : x = \frac{2 πn}{3 - π}

Solve

3 x - x π = π + 2 πn : x = \frac{π}{3 - π} + \frac{2 πn}{3 - π}

x = \frac{2 πn}{3 - π}, x = \frac{π}{3 - π} + \frac{2 πn}{3 - π}

sin^{2} (2 x) = 0.5

sin (x) = - \frac{1}{2} 2

(6 cos (x) + 5 sin (x))^{2} + 11 sin^{2} (x) = 66

- 3 sin (B) - 2 = sin (B) - 2

sin (\frac{θ}{2}) = 2 - sin (\frac{θ}{2})

What is the general solution for tan(3x)=tan(pix) ?
The general solution for tan(3x)=tan(pix) is x=(2pin)/(3-pi),x= pi/(3-pi)+(2pin)/(3-pi)