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

The general solution for 2cos(θ)-2sec(θ)-3=0 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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2cos(θ)-2sec(θ)-3=0

2 cos (θ) - 2 sec (θ) - 3 = 0

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

Solution steps

2 cos (θ) - 2 sec (θ) - 3 = 0

Rewrite using trig identities

- 3 + \frac{2}{sec ( θ )} - 2 sec (θ) = 0

Solve by substitution

sec (θ) = - 2, sec (θ) = \frac{1}{2}

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

sec (θ) = \frac{1}{2} :

No Solution

Combine all the solutions

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

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

sin (θ) = \frac{2}{9}

- 2 sin^{2} (θ) + 9 sin (θ) = 8 sin (θ) - 1

sin^{2} (x) - sin (x) - 1 = 0

2 sec (x) - 4 = 0

What is the general solution for 2cos(θ)-2sec(θ)-3=0 ?
The general solution for 2cos(θ)-2sec(θ)-3=0 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin