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

The general solution for 2sin(x)=cos(x) is x=0.46364…+pin

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2sin(x)=cos(x)

2 sin (x) = cos (x)

x = 0.46364 \dots + πn

Degrees

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 sin (x) = cos (x)

Rewrite using trig identities

2 sin (x) = cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

2 tan (x) = 1

2 tan (x) = 1

Divide both sides by

2

2 tan (x) = 1

Divide both sides by

2

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{1}{2}) + πn

x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = 0.46364 \dots + πn

2 + 2 sin (θ) = 4 cos^{2} (θ)

9 tan (x) sin (x) - 5 sin (x) = 0

x, y = arctan (x)

7 cos (x) + 7 sin (x) tan (x) = 14

cot (θ) + 5 csc (θ) = 6

What is the general solution for 2sin(x)=cos(x) ?
The general solution for 2sin(x)=cos(x) is x=0.46364…+pin