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

The general solution for tan(2x)= 3/4 is x=(0.64350…)/2+(pin)/2

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tan(2x)= 3/4

tan (2 x) = \frac{3}{4}

x = \frac{0.64350 \dots}{2} + \frac{πn}{2}

Degrees

x = 18.43494 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x) = \frac{3}{4}

Apply trig inverse properties

tan (2 x) = \frac{3}{4}

General solutions for

tan (2 x) = \frac{3}{4}

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

2 x = arctan (\frac{3}{4}) + πn

2 x = arctan (\frac{3}{4}) + πn

Solve

2 x = arctan (\frac{3}{4}) + πn : x = \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{3}{4}) + πn

Divide both sides by

2

2 x = arctan (\frac{3}{4}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.64350 \dots}{2} + \frac{πn}{2}

sin (x) = 1 + cos (x)

2 sin (x) = 1 + \frac{cos ( 2 x )}{sin ( x )}

sin (x) = \frac{21}{5}

tan (\frac{θ}{2} - \frac{π}{6}) = 1

1 + 2 sin (θ) = csc (θ)

What is the general solution for tan(2x)= 3/4 ?
The general solution for tan(2x)= 3/4 is x=(0.64350…)/2+(pin)/2