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

The general solution for tan(2x)=sqrt(2) is x=(0.95531…)/2+(pin)/2

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tan(2x)=sqrt(2)

tan (2 x) = 2

x = \frac{0.95531 \dots}{2} + \frac{πn}{2}

Degrees

x = 27.36780 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x) = 2

Apply trig inverse properties

tan (2 x) = 2

General solutions for

tan (2 x) = 2

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

2 x = arctan (2) + πn

2 x = arctan (2) + πn

Solve

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

2 x = arctan (2) + πn

Divide both sides by

2

2 x = arctan (2) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.95531 \dots}{2} + \frac{πn}{2}

\frac{sin ( b )}{13.1} = \frac{sin ( 112. 1 ^{\circ} )}{24.1}

tan (α) = \frac{0.006}{π \cdot 0.027}

sec^{2} (θ) tan (θ) = 2 tan (θ)

tan^{5} (x) + tan^{3} (x) = 0

0 = cos (x) (1 - cos (x)) + sin^{2} (x)

What is the general solution for tan(2x)=sqrt(2) ?
The general solution for tan(2x)=sqrt(2) is x=(0.95531…)/2+(pin)/2