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

The general solution for 2sin(x)tan(2x)-sqrt(3)tan(2x)=0 is x=(pin)/2 ,x= pi/3+2pin,x=(2pi)/3+2pin

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Popular >

2sin(x)tan(2x)-sqrt(3)tan(2x)=0

Solution

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

Solution

x = \frac{πn}{2}, x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Degrees

x = 0^{\circ} + 9 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Factor

2 sin (x) tan (2 x) - 3 tan (2 x) : tan (2 x) (2 sin (x) - 3)

2 sin (x) tan (2 x) - 3 tan (2 x)

Factor out common term

tan (2 x)

= tan (2 x) (2 sin (x) - 3)

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

Solving each part separately

tan (2 x) = 0 or 2 sin (x) - 3 = 0

tan (2 x) = 0 : x = \frac{πn}{2}

tan (2 x) = 0

General solutions for

tan (2 x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

2 x = 0 + πn

2 x = 0 + πn

Solve

2 x = 0 + πn : x = \frac{πn}{2}

2 x = 0 + πn

0 + πn = πn

2 x = πn

Divide both sides by

2

2 x = πn

Divide both sides by

2

\frac{2 x}{2} = \frac{πn}{2}

Simplify

x = \frac{πn}{2}

x = \frac{πn}{2}

x = \frac{πn}{2}

2 sin (x) - 3 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

2 sin (x) - 3 = 0

Move

3

to the right side

2 sin (x) - 3 = 0

Add

3

to both sides

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

Simplify

2 sin (x) = 3

2 sin (x) = 3

Divide both sides by

2

2 sin (x) = 3

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{3}{2}

Simplify

sin (x) = \frac{3}{2}

sin (x) = \frac{3}{2}

General solutions for

sin (x) = \frac{3}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Combine all the solutions

x = \frac{πn}{2}, x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Popular Examples

tan(x)= 12/8

tan (x) = \frac{12}{8}

cos(2t)-cos(t)=-0.5,0<= t<= 2pi

cos (2 t) - cos (t) = - 0.5, 0 \leq t \leq 2 π

3|sin(5θ)|=0

3 ∣ sin (5 θ) ∣ = 0

4cos(x)+6=5(cos(x)+1)

4 cos (x) + 6 = 5 (cos (x) + 1)

cos(x)=0.8736

cos (x) = 0.8736

Frequently Asked Questions (FAQ)

What is the general solution for 2sin(x)tan(2x)-sqrt(3)tan(2x)=0 ?
The general solution for 2sin(x)tan(2x)-sqrt(3)tan(2x)=0 is x=(pin)/2 ,x= pi/3+2pin,x=(2pi)/3+2pin