What is the general solution for 1/(cos(θ))=2 ?

The general solution for 1/(cos(θ))=2 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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1/(cos(θ))=2

\frac{1}{cos ( θ )} = 2

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

Solution steps

\frac{1}{cos ( θ )} = 2

Multiply both sides by

cos (θ)

1 = 2 cos (θ)

Switch sides

2 cos (θ) = 1

Divide both sides by

2

cos (θ) = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

cos (θ) = 0

Combine undefined points with solutions:

cos (θ) = \frac{1}{2}

General solutions for

cos (θ) = \frac{1}{2}

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

θ, r = sin (2 θ)

cos (θ) = \frac{7}{25}, \frac{3 π}{2} < θ < 2 π

5 (1 - sin (θ)) = 5

x, cos (x) = - 1

5 cos (θ) = 5 sin (- θ)

What is the general solution for 1/(cos(θ))=2 ?
The general solution for 1/(cos(θ))=2 is θ= pi/3+2pin,θ=(5pi)/3+2pin