What is the general solution for 3cos(x/2)+sqrt(3)=cos(x/2) ?

The general solution for 3cos(x/2)+sqrt(3)=cos(x/2) is x=(5pi)/3+4pin,x=(7pi)/3+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cos(x/2)+sqrt(3)=cos(x/2)

3 cos (\frac{x}{2}) + 3 = cos (\frac{x}{2})

x = \frac{5 π}{3} + 4 πn, x = \frac{7 π}{3} + 4 πn

Solution steps

3 cos (\frac{x}{2}) + 3 = cos (\frac{x}{2})

Solve by substitution

cos (\frac{x}{2}) = - \frac{3}{2}

cos (\frac{x}{2}) = - \frac{3}{2} : x = \frac{5 π}{3} + 4 πn, x = \frac{7 π}{3} + 4 πn

Combine all the solutions

x = \frac{5 π}{3} + 4 πn, x = \frac{7 π}{3} + 4 πn

(tan (θ) + 1) (tan (θ) - 3) = 0

\frac{2}{3} cos (3 x) = 1

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

csc^{2} (θ) + 5 = 7 - csc (θ)

3 tan^{2} (\frac{x}{3}) - 1 = 0

What is the general solution for 3cos(x/2)+sqrt(3)=cos(x/2) ?
The general solution for 3cos(x/2)+sqrt(3)=cos(x/2) is x=(5pi)/3+4pin,x=(7pi)/3+4pin