What is the general solution for 6cos(3x)=6cos(x) ?

The general solution for 6cos(3x)=6cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6cos(3x)=6cos(x)

6 cos (3 x) = 6 cos (x)

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

Solution steps

6 cos (3 x) = 6 cos (x)

Subtract

6 cos (x)

from both sides

6 cos (3 x) - 6 cos (x) = 0

Rewrite using trig identities

- 24 cos (x) + 24 cos^{3} (x) = 0

Solve by substitution

cos (x) = 0, cos (x) = - 1, cos (x) = 1

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

4 cos (x) = - 22

tan (θ) = \frac{0.15}{0.5}

arctan (\frac{x}{12}) - arctan (x) = 0.001

2 = 2 cos (π + x)

cot (x) + csc (x) cos (x) = 2, cot (x)

What is the general solution for 6cos(3x)=6cos(x) ?
The general solution for 6cos(3x)=6cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin