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

The general solution for 2sin(x)cos(x)-4cos(x)-sin(x)+2=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 >

2sin(x)cos(x)-4cos(x)-sin(x)+2=0

2 sin (x) cos (x) - 4 cos (x) - sin (x) + 2 = 0

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

Solution steps

2 sin (x) cos (x) - 4 cos (x) - sin (x) + 2 = 0

Factor

2 sin (x) cos (x) - 4 cos (x) - sin (x) + 2 : (sin (x) - 2) (2 cos (x) - 1)

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

Solving each part separately

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

sin (x) - 2 = 0 :

No Solution

2 cos (x) - 1 = 0 : 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

\frac{sin ( \frac{π}{2} )}{5} = \frac{sin ( x )}{4}

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

tan^{2} (x) = sec (x) + 1

cos (u) = \frac{2}{5}, cos (2 u)

sin (b) = \frac{2}{2}

What is the general solution for 2sin(x)cos(x)-4cos(x)-sin(x)+2=0 ?
The general solution for 2sin(x)cos(x)-4cos(x)-sin(x)+2=0 is x= pi/3+2pin,x=(5pi)/3+2pin