What is the general solution for 1-cos(x)=2sin^2(x) ?

The general solution for 1-cos(x)=2sin^2(x) is x=2pin,x=(2pi)/3+2pin,x=(4pi)/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)=2sin^2(x)

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

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

Solution steps

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

Subtract

2 sin^{2} (x)

from both sides

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

Rewrite using trig identities

- 1 - cos (x) + 2 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

- cos (x - π) = \frac{3}{2}

cos^{4} (x) = 8 cos^{4} (x) - 8 cos^{2} (x) + 1

sin^{2} (x + \frac{π}{2}) = \frac{3}{4}

sin (2 x - \frac{π}{6}) = \frac{1}{2}

2 cos (x) + 1 = 3 sec (x)

What is the general solution for 1-cos(x)=2sin^2(x) ?
The general solution for 1-cos(x)=2sin^2(x) is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin