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

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

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cos(2θ)-sqrt(3)cos(θ)=0,0<= θ<2pi

cos (2 θ) - 3 cos (θ) = 0, 0 \leq θ < 2 π

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

Solution steps

cos (2 θ) - 3 cos (θ) = 0, 0 \leq θ < 2 π

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}, 0 \leq θ < 2 π :

No Solution

cos (θ) = \frac{3 - 11}{4}, 0 \leq θ < 2 π : θ = arccos (\frac{3 - 11}{4}), θ = - arccos (\frac{3 - 11}{4}) + 2 π

Combine all the solutions

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

Show solutions in decimal form

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

2 cos^{2} (θ) - 7 cos (θ) - 4 = 0

sin (θ) = \frac{3}{10}, sin (θ + \frac{π}{6})

3 sin^{2} (x) = 8 cos (x)

7 cos (x) - 24 sin (x) = 10

4 cos (2 θ) + 1 = 2 cos (θ)

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