What is the general solution for cos(2θ)-sqrt(3)cos(θ)=0 ?

The general solution for cos(2θ)-sqrt(3)cos(θ)=0 is θ=1.97810…+2pin,θ=-1.97810…+2pin

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cos(2θ)-sqrt(3)cos(θ)=0

cos (2 θ) - 3 cos (θ) = 0

θ = 1.97810 \dots + 2 πn, θ = - 1.97810 \dots + 2 πn

Solution steps

cos (2 θ) - 3 cos (θ) = 0

Rewrite using trig identities

- 1 + 2 cos^{2} (θ) - cos (θ) 3 = 0

Solve by substitution

cos (θ) = \frac{3 + 11}{4}, cos (θ) = \frac{3 - 11}{4}

cos (θ) = \frac{3 + 11}{4} :

No Solution

cos (θ) = \frac{3 - 11}{4} : θ = arccos (\frac{3 - 11}{4}) + 2 πn, θ = - arccos (\frac{3 - 11}{4}) + 2 πn

Combine all the solutions

θ = arccos (\frac{3 - 11}{4}) + 2 πn, θ = - arccos (\frac{3 - 11}{4}) + 2 πn

Show solutions in decimal form

θ = 1.97810 \dots + 2 πn, θ = - 1.97810 \dots + 2 πn

tan (x) + sec (x) = 0

cos (θ) = \frac{3}{2}

cos^{2} (θ) + 2 sin (θ) cos (θ) - sin^{2} (θ) = 0

sin (x) - cos (x) = 0, 0 \leq x \leq 2 π

tan (x) + tan^{2} (x) = 0

What is the general solution for cos(2θ)-sqrt(3)cos(θ)=0 ?
The general solution for cos(2θ)-sqrt(3)cos(θ)=0 is θ=1.97810…+2pin,θ=-1.97810…+2pin