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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

cos (x) sin (x) - sin^{2} (x) = 0

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

- 3 sin (x) + 2 = 0

cot (x) = - 0.6

3 sin (x) - cos (x) = 1

tan (x) = - 0.73

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

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