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

The general solution for -2sin(2x)sin(x)=sin(2x) is x=pin,x= pi/2+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-2sin(2x)sin(x)=sin(2x)

Solution

- 2 sin (2 x) sin (x) = sin (2 x)

Solution

x = πn, x = \frac{π}{2} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

- 2 sin (2 x) sin (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

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

Factor

- 2 sin (2 x) sin (x) - sin (2 x) : - sin (2 x) (2 sin (x) + 1)

- 2 sin (2 x) sin (x) - sin (2 x)

Factor out common term

- sin (2 x)

= - sin (2 x) (2 sin (x) + 1)

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

Solving each part separately

sin (2 x) = 0 or 2 sin (x) + 1 = 0

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

sin (2 x) = 0

General solutions for

sin (2 x) = 0

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}

2 x = 0 + 2 πn, 2 x = π + 2 πn

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Divide both sides by

2

2 x = 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplify

x = πn

x = πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Divide both sides by

2

2 x = π + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

2 sin (x) + 1 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin (x) + 1 = 0

Move

1

to the right side

2 sin (x) + 1 = 0

Subtract

1

from both sides

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

Simplify

2 sin (x) = - 1

2 sin (x) = - 1

Divide both sides by

2

2 sin (x) = - 1

Divide both sides by

2

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

Simplify

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

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

General solutions for

sin (x) = - \frac{1}{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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{2} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Popular Examples

2sin(θ)-sqrt(2)=0,0<= θ<= 2pi

2 sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

sin(θ)-0.2cos(θ)=(6.25)/(9.8)

sin (θ) - 0.2 cos (θ) = \frac{6.25}{9.8}

3cos(θ)=8tan(θ)

3 cos (θ) = 8 tan (θ)

tan(θ/4)+sqrt(3)=0

tan (\frac{θ}{4}) + 3 = 0

tan(3r+2)=45

tan (3 r + 2) = 4 5^{\circ}

Frequently Asked Questions (FAQ)

What is the general solution for -2sin(2x)sin(x)=sin(2x) ?
The general solution for -2sin(2x)sin(x)=sin(2x) is x=pin,x= pi/2+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin