What is the general solution for 2cos(2x)+cos(x)-1=0 ?

The general solution for 2cos(2x)+cos(x)-1=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin,x=pi+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn, x = π + 2 πn

Solution steps

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

Rewrite using trig identities

- 3 + cos (x) + 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{3}{4}, cos (x) = - 1

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn, x = π + 2 πn

0.79 = sin (x)

1 + cot (x) = csc (x)

4 cos^{2} (x) - 42 cos (x) + 2 = 0

sin (\frac{2 π}{3} - x) + sin (\frac{2 π}{3} + x) = 0

sin (θ) cos (θ) = cot (θ)

What is the general solution for 2cos(2x)+cos(x)-1=0 ?
The general solution for 2cos(2x)+cos(x)-1=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin,x=pi+2pin