What is the general solution for 2cos^2(θ)-7cos(θ)+3=0 ?

The general solution for 2cos^2(θ)-7cos(θ)+3=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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2cos^2(θ)-7cos(θ)+3=0

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0

Solve by substitution

cos (θ) = 3, cos (θ) = \frac{1}{2}

cos (θ) = 3 :

No Solution

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

sin (x) = 0, 0 \leq x \leq 2 π

tan (x) sin (x) - 4 tan (x) = - 3 tan (x)

7 tan (x) sin (x) - 2 sin (x) = 0

5 sec (x) + 5 tan (x) = 5

4 cos (θ) - 2 = 0

What is the general solution for 2cos^2(θ)-7cos(θ)+3=0 ?
The general solution for 2cos^2(θ)-7cos(θ)+3=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin