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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)sin(x)=sin(x)tan(x)

Solution

3 sin (x) = sin (x) tan (x)

Solution

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

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (x) = sin (x) tan (x)

Subtract

sin (x) tan (x)

from both sides

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

Factor

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

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

Factor out common term

sin (x)

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

3 - tan (x) = 0 : x = \frac{π}{3} + πn

3 - tan (x) = 0

Move

3

to the right side

3 - tan (x) = 0

Subtract

3

from both sides

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

Simplify

- tan (x) = - 3

- tan (x) = - 3

Divide both sides by

- 1

- tan (x) = - 3

Divide both sides by

- 1

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

Simplify

tan (x) = 3

tan (x) = 3

General solutions for

tan (x) = 3

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}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

Combine all the solutions

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

Popular Examples

-2sin(2y)=0

- 2 sin (2 y) = 0

-3+4(cos^2(x))^2+3sin^2(x)=0

- 3 + 4 (cos^{2} (x))^{2} + 3 sin^{2} (x) = 0

4sin(x-30)-1.3=0

4 sin (x - 3 0^{\circ}) - 1.3 = 0

2cos(θ/2)=cos(θ)+1

2 cos (\frac{θ}{2}) = cos (θ) + 1

cos(sqrt(3)x)+sin(sqrt(3)x)=0

cos (3 x) + sin (3 x) = 0

Frequently Asked Questions (FAQ)

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