What is the general solution for cos(2x)-3sin(2x)=0 ?

The general solution for cos(2x)-3sin(2x)=0 is x=(0.32175…)/2+(pin)/2

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cos(2x)-3sin(2x)=0

cos (2 x) - 3 sin (2 x) = 0

x = \frac{0.32175 \dots}{2} + \frac{πn}{2}

Degrees

x = 9.21747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

cos (2 x) - 3 sin (2 x) = 0

Rewrite using trig identities

cos (2 x) - 3 sin (2 x) = 0

Divide both sides by

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

\frac{cos ( 2 x ) - 3 sin ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

1 - \frac{3 sin ( 2 x )}{cos ( 2 x )} = 0

Use the basic trigonometric identity:

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

1 - 3 tan (2 x) = 0

1 - 3 tan (2 x) = 0

Move

1

to the right side

1 - 3 tan (2 x) = 0

Subtract

1

from both sides

1 - 3 tan (2 x) - 1 = 0 - 1

Simplify

- 3 tan (2 x) = - 1

- 3 tan (2 x) = - 1

Divide both sides by

- 3

- 3 tan (2 x) = - 1

Divide both sides by

- 3

\frac{- 3 tan ( 2 x )}{- 3} = \frac{- 1}{- 3}

Simplify

tan (2 x) = \frac{1}{3}

tan (2 x) = \frac{1}{3}

Apply trig inverse properties

tan (2 x) = \frac{1}{3}

General solutions for

tan (2 x) = \frac{1}{3}

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

2 x = arctan (\frac{1}{3}) + πn

2 x = arctan (\frac{1}{3}) + πn

Solve

2 x = arctan (\frac{1}{3}) + πn : x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{1}{3}) + πn

Divide both sides by

2

2 x = arctan (\frac{1}{3}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{1}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.32175 \dots}{2} + \frac{πn}{2}

x, cos (x) + sin (x) = 0

sin (x) (2 cos (x) - 1) = 0

cos (θ) = 1 + 2 sec (θ)

sin (3 θ) = - 1, 0 \leq θ < 2 π

cos (θ) = cos (arctan (\frac{3}{4}))

What is the general solution for cos(2x)-3sin(2x)=0 ?
The general solution for cos(2x)-3sin(2x)=0 is x=(0.32175…)/2+(pin)/2