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

The general solution for cos(x)-sqrt(3)=3cos(x) is x=(5pi)/6+2pin,x=(7pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

cos (x) - 3 = 3 cos (x)

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solution steps

cos (x) - 3 = 3 cos (x)

Solve by substitution

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

cos (x) = - \frac{3}{2} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Combine all the solutions

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

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

sec (x) = 1.86798

2 tan^{2} (x) - 7 sec (x) + 5 = 0

cos (θ) = - \frac{3}{7}

\frac{1}{tan ( x )} + \frac{cos ^{2} ( x )}{sin ( x )} = 0

What is the general solution for cos(x)-sqrt(3)=3cos(x) ?
The general solution for cos(x)-sqrt(3)=3cos(x) is x=(5pi)/6+2pin,x=(7pi)/6+2pin