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

The general solution for 2tan(4x)=1 is x=(0.46364…)/4+(pin)/4

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2tan(4x)=1

2 tan (4 x) = 1

x = \frac{0.46364 \dots}{4} + \frac{πn}{4}

Degrees

x = 6.64126 \dots^{\circ} + 4 5^{\circ} n

Solution steps

2 tan (4 x) = 1

Divide both sides by

2

2 tan (4 x) = 1

Divide both sides by

2

\frac{2 tan ( 4 x )}{2} = \frac{1}{2}

Simplify

tan (4 x) = \frac{1}{2}

tan (4 x) = \frac{1}{2}

Apply trig inverse properties

tan (4 x) = \frac{1}{2}

General solutions for

tan (4 x) = \frac{1}{2}

tan (x) = a \Rightarrow x = arctan (a) + πn

4 x = arctan (\frac{1}{2}) + πn

4 x = arctan (\frac{1}{2}) + πn

Solve

4 x = arctan (\frac{1}{2}) + πn : x = \frac{arctan ( \frac{1}{2} )}{4} + \frac{πn}{4}

4 x = arctan (\frac{1}{2}) + πn

Divide both sides by

4

4 x = arctan (\frac{1}{2}) + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arctan ( \frac{1}{2} )}{4} + \frac{πn}{4}

Simplify

x = \frac{arctan ( \frac{1}{2} )}{4} + \frac{πn}{4}

x = \frac{arctan ( \frac{1}{2} )}{4} + \frac{πn}{4}

x = \frac{arctan ( \frac{1}{2} )}{4} + \frac{πn}{4}

Show solutions in decimal form

x = \frac{0.46364 \dots}{4} + \frac{πn}{4}

cos (θ) = \frac{5713634.83}{( 2236 ) ( 3733 )}

sin (x) = \frac{3}{58}

cos (2 x + 1) = 0

cos (4 x) = \frac{- 3}{2}

(sec (x))^{2} = 0

What is the general solution for 2tan(4x)=1 ?
The general solution for 2tan(4x)=1 is x=(0.46364…)/4+(pin)/4