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

The general solution for cos(x)tan^2(x)=3cos(x) is 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 >

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

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

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

Solution steps

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

Subtract

3 cos (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

Since the equation is undefined for:

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

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

cos (x) = 0.52

sec^{2} (x) - 2 sec (x) = 0

- 9 tan^{2} (θ) - 1 = - 6 tan (θ)

2 cos (2 θ) - 1 = 0

4 cos (2 x) - 1 = 0

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