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

The general solution for 2cos^2(x)=3cos(x)-1 is x=2pin,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^2(x)=3cos(x)-1

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

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

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

sin^{2} (x) - 4 sin (x) + 4 = 0

3 cos^{2} (x) - 10 cos (x) + 3 = 0

(m + 1) sin (x) + 2 - m = 0

sin^{5} (x) + sin (x) + 2 sin^{2} (x) = 1

(2 cos (x) - 1) \cdot (2 sin (x) + 1) = 3 - 4 sin^{2} (x)

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