What is the general solution for 5cos(x)=5cos(2x) ?

The general solution for 5cos(x)=5cos(2x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5cos(x)=5cos(2x)

5 cos (x) = 5 cos (2 x)

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

Solution steps

5 cos (x) = 5 cos (2 x)

Subtract

5 cos (2 x)

from both sides

5 cos (x) - 5 cos (2 x) = 0

Rewrite using trig identities

- (- 1 + 2 cos^{2} (x)) \cdot 5 + 5 cos (x) = 0

Solve by substitution

cos (x) = - \frac{1}{2}, cos (x) = 1

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

cos (4 θ) = cos (2 θ)

3 cos (3 x) = 2

sec (θ) - 2 = - tan (θ) - 3

sin^{2} (x) - sin (x) = 1

2 sin (x) cos (x) + 1 sin (x) = 0

What is the general solution for 5cos(x)=5cos(2x) ?
The general solution for 5cos(x)=5cos(2x) is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin