What is the general solution for tan(2θ)=2 ?

The general solution for tan(2θ)=2 is θ=(1.10714…)/2+(pin)/2

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tan(2θ)=2

tan (2 θ) = 2

θ = \frac{1.10714 \dots}{2} + \frac{πn}{2}

Degrees

θ = 31.71747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 2

Apply trig inverse properties

tan (2 θ) = 2

General solutions for

tan (2 θ) = 2

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

2 θ = arctan (2) + πn

2 θ = arctan (2) + πn

Solve

2 θ = arctan (2) + πn : θ = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

2 θ = arctan (2) + πn

Divide both sides by

2

2 θ = arctan (2) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{1.10714 \dots}{2} + \frac{πn}{2}

12 sin^{3} (x) - 9 sin (x) = 0

cos (3 0^{\circ} + x) - sin (x) = 0

53 cos (x) - 10 sin (x) cos (x) = 0

tan (x) = \frac{5}{20}

cos (x) (1 + 2 sin (x)) = 0

What is the general solution for tan(2θ)=2 ?
The general solution for tan(2θ)=2 is θ=(1.10714…)/2+(pin)/2