What is the general solution for 3cos^2(x)-sin^2(x)=0 ?

The general solution for 3cos^2(x)-sin^2(x)=0 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 >

3cos^2(x)-sin^2(x)=0

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

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

Solution steps

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

cos (x) = - 0.6

cos (x) = - 0.9

2 cos (x) + 3 sin (x) = 0

sec (\frac{x}{5}) = 10

csc (x) = - 3

What is the general solution for 3cos^2(x)-sin^2(x)=0 ?
The general solution for 3cos^2(x)-sin^2(x)=0 is x=(2pi)/3+pin,x= pi/3+pin