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

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

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2sin(x)=4cos(x)

2 sin (x) = 4 cos (x)

x = 1.10714 \dots + πn

Degrees

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

Solution steps

2 sin (x) = 4 cos (x)

Rewrite using trig identities

2 sin (x) = 4 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

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

6 arcsin (x) = 2 π

8 cos (x) = 0

2 sin (x) \cdot tan (x) + 5 sin (x) = - 2 cos (x)

2 cot (x) sin (x) + cot (x) = 0

2 sin (x) - (2 + 3) = - 3 csc (x)

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