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

The general solution for 2cos^2(x)+sqrt(3)cos(x)-3=0 is x= pi/6+2pin,x=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

cos (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

cos (2 x) = \frac{2}{2}, 0 \leq x \leq 2 π

sin (2 x) cos (x) = 0

8 cos (x) + 8 sin (x) tan (x) = 16

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

What is the general solution for 2cos^2(x)+sqrt(3)cos(x)-3=0 ?
The general solution for 2cos^2(x)+sqrt(3)cos(x)-3=0 is x= pi/6+2pin,x=(11pi)/6+2pin