What is the general solution for sin(2x)=4cos(2x) ?

The general solution for sin(2x)=4cos(2x) is x=(1.32581…)/2+(pin)/2

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sin(2x)=4cos(2x)

sin (2 x) = 4 cos (2 x)

x = \frac{1.32581 \dots}{2} + \frac{πn}{2}

Degrees

x = 37.98187 \dots^{\circ} + 9 0^{\circ} n

Solution steps

sin (2 x) = 4 cos (2 x)

Rewrite using trig identities

sin (2 x) = 4 cos (2 x)

Divide both sides by

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

\frac{sin ( 2 x )}{cos ( 2 x )} = \frac{4 cos ( 2 x )}{cos ( 2 x )}

Simplify

\frac{sin ( 2 x )}{cos ( 2 x )} = 4

Use the basic trigonometric identity:

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

tan (2 x) = 4

tan (2 x) = 4

Apply trig inverse properties

tan (2 x) = 4

General solutions for

tan (2 x) = 4

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

2 x = arctan (4) + πn

2 x = arctan (4) + πn

Solve

2 x = arctan (4) + πn : x = \frac{arctan ( 4 )}{2} + \frac{πn}{2}

2 x = arctan (4) + πn

Divide both sides by

2

2 x = arctan (4) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( 4 )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( 4 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 4 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 4 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.32581 \dots}{2} + \frac{πn}{2}

- 9 cos^{2} (θ) + 1 = sin (θ)

1 - sin (θ) = sin (θ)

cot (\frac{θ}{3} + \frac{3 π}{4}) = 3

cos (x) = \frac{tan ( x ) + cot ( x )}{csc ( x )}

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

What is the general solution for sin(2x)=4cos(2x) ?
The general solution for sin(2x)=4cos(2x) is x=(1.32581…)/2+(pin)/2