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

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

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1+1/(cos(x))=0

Solution

1 + \frac{1}{cos ( x )} = 0

Solution

x = π + 2 πn

Degrees

x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

1 + \frac{1}{cos ( x )} = 0

Multiply both sides by

cos (x)

1 + \frac{1}{cos ( x )} = 0

Multiply both sides by

cos (x)

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

Simplify

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

Simplify

1 \cdot cos (x) : cos (x)

1 \cdot cos (x)

Multiply:

1 \cdot cos (x) = cos (x)

= 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

cos (x) + 1 = 0

cos (x) + 1 = 0

cos (x) + 1 = 0

Move

1

to the right side

cos (x) + 1 = 0

Subtract

1

from both sides

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

Simplify

cos (x) = - 1

cos (x) = - 1

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Take the denominator(s) of

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

and compare to zero

cos (x) = 0

The following points are undefined

cos (x) = 0

Combine undefined points with solutions:

cos (x) = - 1

General solutions for

cos (x) = - 1

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 = π + 2 πn

x = π + 2 πn

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9=-9*sin(2x)

9 = - 9 \cdot sin (2 x)

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a^{1} sin (x) = 43.1253

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52800 = \frac{( 1500 ) ^{2} sin ( x )}{32.2}

Frequently Asked Questions (FAQ)

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