What is the general solution for cos(2x)+3cos(x)=-2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Subtract

- 2

from both sides

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

Rewrite using trig identities

1 + 2 cos^{2} (x) + 3 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 = π + 2 πn

Combine all the solutions

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

4 tan^{2} (θ) + 16 tan (θ) = 7 tan (θ) - 2

10 (1 - cos (θ)) = sin^{2} (θ)

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

tan (x - 20) = cot (x + 45)

sin (z) = 4

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