What is the general solution for 2tan(4x)+1=3tan(4x) ?

The general solution for 2tan(4x)+1=3tan(4x) is x= pi/(16)+(pin)/4

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2tan(4x)+1=3tan(4x)

2 tan (4 x) + 1 = 3 tan (4 x)

x = \frac{π}{16} + \frac{πn}{4}

Solution steps

2 tan (4 x) + 1 = 3 tan (4 x)

Solve by substitution

tan (4 x) = 1

tan (4 x) = 1 : x = \frac{π}{16} + \frac{πn}{4}

Combine all the solutions

x = \frac{π}{16} + \frac{πn}{4}

sec (x) = - 5, π < x < \frac{3 π}{2}

sin (\frac{θ}{2}) = \frac{3}{5}

2 sin^{3} (t) + sin^{2} (t) - 2 sin (t) - 1 = 0

sin (x) = \frac{1}{5}, cos (x) > 0

2 sin^{2} (2 θ) = - 1 - 3 sin (2 θ)

What is the general solution for 2tan(4x)+1=3tan(4x) ?
The general solution for 2tan(4x)+1=3tan(4x) is x= pi/(16)+(pin)/4