What is the general solution for 2cos^3(x)-cos^2(x)+2cos(x)-1=0 ?

The general solution for 2cos^3(x)-cos^2(x)+2cos(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos^3(x)-cos^2(x)+2cos(x)-1=0

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

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

Solution steps

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

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = i :

No Solution

cos (x) = - i :

No Solution

Combine all the solutions

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

x, - 44 sin (2 x) + 42 cos (2 x) = 0

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

sin (x) = \frac{2 π}{3}

cos (3 x) + sin (2 x) + cos (x) = 0

tan (2 θ) = 1.333

What is the general solution for 2cos^3(x)-cos^2(x)+2cos(x)-1=0 ?
The general solution for 2cos^3(x)-cos^2(x)+2cos(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin