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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(θ)cos(θ)=cos(θ)

sin^{2} (θ) cos (θ) = cos (θ)

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

Solution steps

sin^{2} (θ) cos (θ) = cos (θ)

Subtract

cos (θ)

from both sides

sin^{2} (θ) cos (θ) - cos (θ) = 0

Factor

sin^{2} (θ) cos (θ) - cos (θ) : cos (θ) (sin (θ) + 1) (sin (θ) - 1)

cos (θ) (sin (θ) + 1) (sin (θ) - 1) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) + 1 = 0 or sin (θ) - 1 = 0

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

sin (θ) + 1 = 0 : θ = \frac{3 π}{2} + 2 πn

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

Combine all the solutions

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

cos (3 0^{\circ} + x) = 276

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

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

tan^{2} (\frac{x}{2}) = 1

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

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