What is the general solution for tan^2(x)sin(x)=3sin(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan^2(x)sin(x)=3sin(x)

tan^{2} (x) sin (x) = 3 sin (x)

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

Solution steps

tan^{2} (x) sin (x) = 3 sin (x)

Subtract

3 sin (x)

from both sides

tan^{2} (x) sin (x) - 3 sin (x) = 0

Factor

tan^{2} (x) sin (x) - 3 sin (x) : sin (x) (tan (x) + 3) (tan (x) - 3)

sin (x) (tan (x) + 3) (tan (x) - 3) = 0

Solving each part separately

sin (x) = 0 or tan (x) + 3 = 0 or tan (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

tan (x) - 3 = 0 : x = \frac{π}{3} + πn

Combine all the solutions

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

cos (θ) - sin (2 θ) = 0

sin (7 x) = 0

cos (2 x) - 3 cos (x) = - 1

x, tan (x) = - 1

2 sin (x) = 3 cos (x)

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