What is the general solution for 2cos(x/2)=1 ?

The general solution for 2cos(x/2)=1 is x=(2pi)/3+4pin,x=(10pi)/3+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(x/2)=1

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

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Solution steps

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

Divide both sides by

2

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

General solutions for

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

\frac{x}{2} = \frac{π}{3} + 2 πn, \frac{x}{2} = \frac{5 π}{3} + 2 πn

Solve

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

Solve

\frac{x}{2} = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

cos (x) = \frac{6}{10}

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

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

cos (3 x) = - sin (x + \frac{π}{6})

sin (θ) = \frac{7}{10}

What is the general solution for 2cos(x/2)=1 ?
The general solution for 2cos(x/2)=1 is x=(2pi)/3+4pin,x=(10pi)/3+4pin