What is the general solution for 1/(cos(x))=4 ?

The general solution for 1/(cos(x))=4 is x=1.31811…+2pin,x=2pi-1.31811…+2pin

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1/(cos(x))=4

\frac{1}{cos ( x )} = 4

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Solution steps

\frac{1}{cos ( x )} = 4

Multiply both sides by

cos (x)

1 = 4 cos (x)

Switch sides

4 cos (x) = 1

Divide both sides by

4

cos (x) = \frac{1}{4}

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Combine undefined points with solutions:

cos (x) = \frac{1}{4}

Apply trig inverse properties

x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

sin (θ) = - 0.15

2 cos (4 x) = 1

cos (2 x) = 2 sin (2 x)

4 cos^{2} (x) - 1 = 1

2 sin (θ) - 1 = 0

What is the general solution for 1/(cos(x))=4 ?
The general solution for 1/(cos(x))=4 is x=1.31811…+2pin,x=2pi-1.31811…+2pin