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

The general solution for solvefor x,y-1/(cos(x))=0 is x=arccos(1/y)+2pin,x=-arccos(1/y)+2pin

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solvefor x,y-1/(cos(x))=0

solve for

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

x = arccos (\frac{1}{y}) + 2 πn, x = - arccos (\frac{1}{y}) + 2 πn

Solution steps

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

Multiply both sides by

cos (x)

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

Multiply both sides by

cos (x)

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

Simplify

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

y cos (x) - 1 = 0

y cos (x) - 1 = 0

y cos (x) - 1 = 0

Move

1

to the right side

y cos (x) - 1 = 0

Add

1

to both sides

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

Simplify

y cos (x) = 1

y cos (x) = 1

Divide both sides by

y; y \neq = 0

y cos (x) = 1

Divide both sides by

y; y \neq = 0

\frac{y cos ( x )}{y} = \frac{1}{y}; y \neq = 0

Simplify

cos (x) = \frac{1}{y}; y \neq = 0

cos (x) = \frac{1}{y}; y \neq = 0

Apply trig inverse properties

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

General solutions for

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

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (\frac{1}{y}) + 2 πn, x = - arccos (\frac{1}{y}) + 2 πn

x = arccos (\frac{1}{y}) + 2 πn, x = - arccos (\frac{1}{y}) + 2 πn

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

sin^{2} (x) sec (x) = tan^{2} (x)

cos (2 x + \frac{π}{3}) = - \frac{1}{2}

sec (θ + 2 0^{\circ}) = 3

tan (θ) = \frac{7.7}{14}

What is the general solution for solvefor x,y-1/(cos(x))=0 ?
The general solution for solvefor x,y-1/(cos(x))=0 is x=arccos(1/y)+2pin,x=-arccos(1/y)+2pin