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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Subtract

2 cos (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

sin (x) - 2 = 0 :

No Solution

Combine all the solutions

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

tan^{2} (x) + 5 tan (x) + 6 = 0

cos^{4} (x) - sin^{4} (x) = 1

4 sec^{2} (x) tan (x) = 8 tan (x)

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

tan (2 x) = tan (x)

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