2= 1/(cos^2(x))

Solution

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

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

Solution steps

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

Switch sides

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

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

arccot (x - 2) = arccot (x - 1) + arccot (x)

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

sin (x) + 3 cos (x) = 2

arccos (2 x) = π

\frac{cosh ( 0.2 m )}{cosh ( 0.4 m )} = 0.6