What is the general solution for 3tan(2x)=5 ?

The general solution for 3tan(2x)=5 is x=(1.03037…)/2+(pin)/2

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3tan(2x)=5

3 tan (2 x) = 5

x = \frac{1.03037 \dots}{2} + \frac{πn}{2}

Degrees

x = 29.51812 \dots^{\circ} + 9 0^{\circ} n

Solution steps

3 tan (2 x) = 5

Divide both sides by

3

3 tan (2 x) = 5

Divide both sides by

3

\frac{3 tan ( 2 x )}{3} = \frac{5}{3}

Simplify

tan (2 x) = \frac{5}{3}

tan (2 x) = \frac{5}{3}

Apply trig inverse properties

tan (2 x) = \frac{5}{3}

General solutions for

tan (2 x) = \frac{5}{3}

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

2 x = arctan (\frac{5}{3}) + πn

2 x = arctan (\frac{5}{3}) + πn

Solve

2 x = arctan (\frac{5}{3}) + πn : x = \frac{arctan ( \frac{5}{3} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{5}{3}) + πn

Divide both sides by

2

2 x = arctan (\frac{5}{3}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{5}{3} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{5}{3} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{5}{3} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{5}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.03037 \dots}{2} + \frac{πn}{2}

3 - 2 cos (θ) = 3 - 2 sin (θ)

(4 cos (x) - 2 sin (x))^{2} + 12 sin^{2} (x) = 16

arcsin (x) = π

y = sin (2 x), x

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

What is the general solution for 3tan(2x)=5 ?
The general solution for 3tan(2x)=5 is x=(1.03037…)/2+(pin)/2