What is the general solution for 2sin(x)cos(x)+2sin(x)-cos(x)-1=0 ?

The general solution for 2sin(x)cos(x)+2sin(x)-cos(x)-1=0 is x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+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)+2sin(x)-cos(x)-1=0

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

x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Factor

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

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

Solving each part separately

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

cos (x) + 1 = 0 : x = π + 2 πn

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (θ) tan^{2} (θ) - sin (θ) = 0

sin (x) = \frac{4}{5}, sin (18 0^{\circ} - x)

- 11 cos (x) (22) - 11 sin (x) (8) = - 250

3 cos (x) + 1 = 2 sin (x)

\frac{π}{6} = cos (2 x)

What is the general solution for 2sin(x)cos(x)+2sin(x)-cos(x)-1=0 ?
The general solution for 2sin(x)cos(x)+2sin(x)-cos(x)-1=0 is x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin