What is the general solution for sin(2x)cos(x)=cos(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)cos(x)=cos(x)

sin (2 x) cos (x) = cos (x)

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

Solution steps

sin (2 x) cos (x) = cos (x)

Subtract

cos (x)

from both sides

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

Factor

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

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

Solving each part separately

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (2 x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

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

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

cos (x) = \frac{7}{16}

3 = - 2 cos (θ)

4 sin (3 x) = 2

3 sin (4 x) = 23

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