What is the general solution for 2cos^2(θ)=cos(θ)+1 ?

The general solution for 2cos^2(θ)=cos(θ)+1 is θ=2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos^2(θ)=cos(θ)+1

2 cos^{2} (θ) = cos (θ) + 1

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

Solution steps

2 cos^{2} (θ) = cos (θ) + 1

Solve by substitution

cos (θ) = 1, cos (θ) = - \frac{1}{2}

cos (θ) = 1 : θ = 2 πn

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

Combine all the solutions

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

tan (θ) = \frac{100}{101}

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

10 tan (b) + 12 = tan (b) + 6

arctan (x) + arctan (1 - x) = arctan (\frac{4}{3})

cos (θ) = \frac{- 8}{14 \cdot 20}

What is the general solution for 2cos^2(θ)=cos(θ)+1 ?
The general solution for 2cos^2(θ)=cos(θ)+1 is θ=2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin