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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Popular >

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

Solution

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

Solution

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Multiply both sides by

cos (x)

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

Multiply both sides by

cos (x)

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

Simplify

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

Simplify

\frac{1}{cos ( x )} cos (x) : 1

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

cos (x)

= 1

Simplify

0 \cdot cos (x) : 0

0 \cdot cos (x)

Apply rule

0 \cdot a = 0

= 0

1 - 2 cos (x) = 0

1 - 2 cos (x) = 0

1 - 2 cos (x) = 0

Move

1

to the right side

1 - 2 cos (x) = 0

Subtract

1

from both sides

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

Simplify

- 2 cos (x) = - 1

- 2 cos (x) = - 1

Divide both sides by

- 2

- 2 cos (x) = - 1

Divide both sides by

- 2

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

Simplify

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

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

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Take the denominator(s) of

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

and compare to zero

cos (x) = 0

The following points are undefined

cos (x) = 0

Combine undefined points with solutions:

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

General solutions for

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

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Popular Examples

6cos(6x-pi/4)+3=0

6 cos (6 x - \frac{π}{4}) + 3 = 0

-1=sec(θ)

- 1 = sec (θ)

sin(a)= 20/30

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

sin(θ+15)= 2/3

sin (θ + 1 5^{\circ}) = \frac{2}{3}

solvefor θ,2sin(θ)-1=0 solve for

θ, 2 sin (θ) - 1 = 0

Frequently Asked Questions (FAQ)

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