What is the general solution for 1-4tan(3x+1)=17 ?

The general solution for 1-4tan(3x+1)=17 is x=-(1.32581…)/3+(pin)/3-1/3

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1-4tan(3x+1)=17

1 - 4 tan (3 x + 1) = 17

x = - \frac{1.32581 \dots}{3} + \frac{πn}{3} - \frac{1}{3}

Solution steps

1 - 4 tan (3 x + 1) = 17

Move

1

to the right side

- 4 tan (3 x + 1) = 16

Divide both sides by

- 4

tan (3 x + 1) = - 4

Apply trig inverse properties

3 x + 1 = arctan (- 4) + πn

Solve

3 x + 1 = arctan (- 4) + πn : x = - \frac{arctan ( 4 )}{3} + \frac{πn}{3} - \frac{1}{3}

x = - \frac{arctan ( 4 )}{3} + \frac{πn}{3} - \frac{1}{3}

Show solutions in decimal form

x = - \frac{1.32581 \dots}{3} + \frac{πn}{3} - \frac{1}{3}

sin (x) cos (x) + sin (x) = 3 cos^{2} (x) + 3 cos (x)

2 - 2 sin^{2} (x) = - 3 cos (x) + 2

4 tan (θ) + 7 = 0

arctan (x) + arctan (3 x) + arctan (7 x) = 18 0^{\circ}

2 cos (a) = 1

What is the general solution for 1-4tan(3x+1)=17 ?
The general solution for 1-4tan(3x+1)=17 is x=-(1.32581…)/3+(pin)/3-1/3