What is the general solution for 1-cos(x)=sqrt(3)sin(x) ?

The general solution for 1-cos(x)=sqrt(3)sin(x) is x=2pin,x=(2pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1-cos(x)=sqrt(3)sin(x)

1 - cos (x) = 3 sin (x)

x = 2 πn, x = \frac{2 π}{3} + 2 πn

Solution steps

1 - cos (x) = 3 sin (x)

Square both sides

(1 - cos (x))^{2} = (3 sin (x))^{2}

Subtract

(3 sin (x))^{2}

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = - \frac{1}{2}

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Verify solutions by plugging them into the original equation

x = 2 πn, x = \frac{2 π}{3} + 2 πn

sin (θ) = \frac{7}{25}

tan (x) = \frac{4}{5}

6 sec (x) csc (x) = 12 csc (x)

2 tan^{2} (θ) + 3 tan (θ) = 0

tan (x) + cot (x) = 2

What is the general solution for 1-cos(x)=sqrt(3)sin(x) ?
The general solution for 1-cos(x)=sqrt(3)sin(x) is x=2pin,x=(2pi)/3+2pin