What is the general solution for 3sin(2x)=cos(2x) ?

The general solution for 3sin(2x)=cos(2x) is x=(0.32175…)/2+(pin)/2

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3sin(2x)=cos(2x)

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

x = \frac{0.32175 \dots}{2} + \frac{πn}{2}

Degrees

x = 9.21747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{3 sin ( 2 x )}{cos ( 2 x )} = \frac{cos ( 2 x )}{cos ( 2 x )}

Simplify

\frac{3 sin ( 2 x )}{cos ( 2 x )} = 1

Use the basic trigonometric identity:

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

3 tan (2 x) = 1

3 tan (2 x) = 1

Divide both sides by

3

3 tan (2 x) = 1

Divide both sides by

3

\frac{3 tan ( 2 x )}{3} = \frac{1}{3}

Simplify

tan (2 x) = \frac{1}{3}

tan (2 x) = \frac{1}{3}

Apply trig inverse properties

tan (2 x) = \frac{1}{3}

General solutions for

tan (2 x) = \frac{1}{3}

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

2 x = arctan (\frac{1}{3}) + πn

2 x = arctan (\frac{1}{3}) + πn

Solve

2 x = arctan (\frac{1}{3}) + πn : x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{1}{3}) + πn

Divide both sides by

2

2 x = arctan (\frac{1}{3}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.32175 \dots}{2} + \frac{πn}{2}

3 \cdot 2 = \frac{50 sin ( x )}{9.8}

cos (2 x + 5) = sin (2 x)

sin (2 θ) + 3 cos (θ) = cos (θ)

1 + cos (θ) = 1 + sin (θ)

500 = 538 cos (x - 1 0^{\circ})

What is the general solution for 3sin(2x)=cos(2x) ?
The general solution for 3sin(2x)=cos(2x) is x=(0.32175…)/2+(pin)/2