What is the general solution for cos(2x)-5cos(x)+3=0 ?

The general solution for cos(2x)-5cos(x)+3=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 >

cos(2x)-5cos(x)+3=0

cos (2 x) - 5 cos (x) + 3 = 0

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

Solution steps

cos (2 x) - 5 cos (x) + 3 = 0

Rewrite using trig identities

2 + 2 cos^{2} (x) - 5 cos (x) = 0

Solve by substitution

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

cos (x) = 2 :

No Solution

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

Combine all the solutions

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

9 sin^{2} (x) + 18 sin (x) + 9 = 0

- 12 sin^{2} (θ) + 7 = 4

4 cos (θ) + 5 = 0

cos (θ) = \frac{60}{78}

18 sin^{2} (x) = 9

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