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

The general solution for 4cos(x)=2sin(x) is x=1.10714…+pin

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4cos(x)=2sin(x)

4 cos (x) = 2 sin (x)

x = 1.10714 \dots + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 cos (x) = 2 sin (x)

Rewrite using trig identities

4 cos (x) = 2 sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

4 = 2 tan (x)

Switch sides

2 tan (x) = 4

2 tan (x) = 4

Divide both sides by

2

2 tan (x) = 4

Divide both sides by

2

\frac{2 tan ( x )}{2} = \frac{4}{2}

Simplify

tan (x) = 2

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

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

x = arctan (2) + πn

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

What is the general solution for 4cos(x)=2sin(x) ?
The general solution for 4cos(x)=2sin(x) is x=1.10714…+pin