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

The general solution for sin(2x)=3cos(2x) is x=(1.24904…)/2+(pin)/2

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

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

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

Degrees

x = 35.78252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (2 x) = 3

tan (2 x) = 3

Apply trig inverse properties

tan (2 x) = 3

General solutions for

tan (2 x) = 3

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

2 x = arctan (3) + πn

2 x = arctan (3) + πn

Solve

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

2 x = arctan (3) + πn

Divide both sides by

2

2 x = arctan (3) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

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

cos (2 x) - sin (x) = 1

sec (3 x) = - 1

2 cos^{2} (x) + 1 = 3 cos (x)

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

tan (2 θ) = 0

What is the general solution for sin(2x)=3cos(2x) ?
The general solution for sin(2x)=3cos(2x) is x=(1.24904…)/2+(pin)/2