What is the general solution for 4cos^2(x)-4cos(x)-3=0 ?

The general solution for 4cos^2(x)-4cos(x)-3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(x)-4cos(x)-3=0

4 cos^{2} (x) - 4 cos (x) - 3 = 0

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

Solution steps

4 cos^{2} (x) - 4 cos (x) - 3 = 0

Solve by substitution

cos (x) = \frac{3}{2}, cos (x) = - \frac{1}{2}

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

No Solution

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

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

cot (x) = \frac{4}{3}

tan (θ) = - \frac{5}{2}

- 1 = cos (t) + cos (2 t)

15 cos (3 x) = 0

- \frac{1}{2} = sin (2 x)

What is the general solution for 4cos^2(x)-4cos(x)-3=0 ?
The general solution for 4cos^2(x)-4cos(x)-3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin