What is the general solution for 1/(cos(x))-2=0 ?

The general solution for 1/(cos(x))-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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1/(cos(x))-2=0

\frac{1}{cos ( x )} - 2 = 0

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

Solution steps

\frac{1}{cos ( x )} - 2 = 0

Multiply both sides by

cos (x)

1 - 2 cos (x) = 0

Move

1

to the right side

- 2 cos (x) = - 1

Divide both sides by

- 2

cos (x) = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Combine undefined points with solutions:

cos (x) = \frac{1}{2}

General solutions for

cos (x) = \frac{1}{2}

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

6 cos (6 x - \frac{π}{4}) + 3 = 0

- 1 = sec (θ)

sin (a) = \frac{20}{30}

sin (θ + 1 5^{\circ}) = \frac{2}{3}

θ, 2 sin (θ) - 1 = 0

What is the general solution for 1/(cos(x))-2=0 ?
The general solution for 1/(cos(x))-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin