What is the general solution for 2sin(2x)=cos(2x) ?

The general solution for 2sin(2x)=cos(2x) is x=(0.46364…)/2+(pin)/2

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2sin(2x)=cos(2x)

2 sin (2 x) = cos (2 x)

x = \frac{0.46364 \dots}{2} + \frac{πn}{2}

Degrees

x = 13.28252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 sin (2 x) = cos (2 x)

Rewrite using trig identities

2 sin (2 x) = cos (2 x)

Divide both sides by

cos (2 x), cos (2 x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

2 tan (2 x) = 1

2 tan (2 x) = 1

Divide both sides by

2

2 tan (2 x) = 1

Divide both sides by

2

\frac{2 tan ( 2 x )}{2} = \frac{1}{2}

Simplify

tan (2 x) = \frac{1}{2}

tan (2 x) = \frac{1}{2}

Apply trig inverse properties

tan (2 x) = \frac{1}{2}

General solutions for

tan (2 x) = \frac{1}{2}

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

2 x = arctan (\frac{1}{2}) + πn

2 x = arctan (\frac{1}{2}) + πn

Solve

2 x = arctan (\frac{1}{2}) + πn : x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{1}{2}) + πn

Divide both sides by

2

2 x = arctan (\frac{1}{2}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.46364 \dots}{2} + \frac{πn}{2}

sin (2 θ) = 3

1 2^{2} = 1 5^{2} + 2 0^{2} - 2 (15) (20) (cos (a))

0.428 = cos (1.57 \cdot x - π)

5 = 10 sin (a)

sin (θ) = cos (2 θ + 5 4^{\circ})

What is the general solution for 2sin(2x)=cos(2x) ?
The general solution for 2sin(2x)=cos(2x) is x=(0.46364…)/2+(pin)/2