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

The general solution for tan(2θ)=3 is θ=(1.24904…)/2+(pin)/2

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tan(2θ)=3

tan (2 θ) = 3

θ = \frac{1.24904 \dots}{2} + \frac{πn}{2}

Solution steps

tan (2 θ) = 3

Apply trig inverse properties

2 θ = arctan (3) + πn

Solve

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

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

Show solutions in decimal form

θ = \frac{1.24904 \dots}{2} + \frac{πn}{2}

sin^{2} (x) - 6 cos (x) - 6 = 0

(3 tan^{2} (x) - 1) = 0

8 sin (\frac{x}{2}) - 8 = 0

cos (2 x) + 2 = 3 cos (x)

cos (x) = - cos (2 x)

What is the general solution for tan(2θ)=3 ?
The general solution for tan(2θ)=3 is θ=(1.24904…)/2+(pin)/2