What is the general solution for 0=-2sin(2x)+cos(2x) ?

The general solution for 0=-2sin(2x)+cos(2x) is x=(0.46364…)/2+(pin)/2

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0=-2sin(2x)+cos(2x)

0 = - 2 sin (2 x) + cos (2 x)

x = \frac{0.46364 \dots}{2} + \frac{πn}{2}

Degrees

x = 13.28252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

0 = - 2 sin (2 x) + cos (2 x)

Switch sides

- 2 sin (2 x) + cos (2 x) = 0

Rewrite using trig identities

- 2 sin (2 x) + cos (2 x) = 0

Divide both sides by

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

\frac{- 2 sin ( 2 x ) + cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

- \frac{2 sin ( 2 x )}{cos ( 2 x )} + 1 = 0

Use the basic trigonometric identity:

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

- 2 tan (2 x) + 1 = 0

- 2 tan (2 x) + 1 = 0

Move

1

to the right side

- 2 tan (2 x) + 1 = 0

Subtract

1

from both sides

- 2 tan (2 x) + 1 - 1 = 0 - 1

Simplify

- 2 tan (2 x) = - 1

- 2 tan (2 x) = - 1

Divide both sides by

- 2

- 2 tan (2 x) = - 1

Divide both sides by

- 2

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

2 x = arctan (\frac{1}{2}) + πn

2 x = arctan (\frac{1}{2}) + πn

Solve

2 x = arctan (\frac{1}{2}) + πn : x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{1}{2}) + πn

Divide both sides by

2

2 x = arctan (\frac{1}{2}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.46364 \dots}{2} + \frac{πn}{2}

y, arcsin (y) = arcsin (x)

4 csc (x) + 2 sin (x) = 9

x, h = 1 + sin (π x)

1 - cos (θ) = sin (\frac{θ}{2})

cos (\frac{θ}{3} + 2 4^{\circ}) = sin (θ)

What is the general solution for 0=-2sin(2x)+cos(2x) ?
The general solution for 0=-2sin(2x)+cos(2x) is x=(0.46364…)/2+(pin)/2