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

The general solution for sec(θ)=2cos(θ) is θ= pi/4+2pin,θ=(7pi)/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin

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sec(θ)=2cos(θ)

sec (θ) = 2 cos (θ)

θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Solution steps

sec (θ) = 2 cos (θ)

Subtract

2 cos (θ)

from both sides

sec (θ) - 2 cos (θ) = 0

Rewrite using trig identities

- \frac{2}{sec ( θ )} + sec (θ) = 0

Solve by substitution

sec (θ) = 2, sec (θ) = - 2

sec (θ) = 2 : θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

sec (θ) = - 2 : θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Combine all the solutions

θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

2 sin^{2} (x) + 3 sin (x) = 0

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

arccos (x) + 2 arcsin (\frac{3}{2}) = π

3 - 3 sin (θ) = 2 cos^{2} (θ)

tan (a) = - 3

What is the general solution for sec(θ)=2cos(θ) ?
The general solution for sec(θ)=2cos(θ) is θ= pi/4+2pin,θ=(7pi)/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin