What is the general solution for sec(x)=sqrt(1-tan^2(x)) ?

The general solution for sec(x)=sqrt(1-tan^2(x)) is x=2pin

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sec(x)=sqrt(1-tan^2(x))

sec (x) = 1 - tan^{2} (x)

x = 2 πn

Solution steps

sec (x) = 1 - tan^{2} (x)

Subtract

1 - tan^{2} (x)

from both sides

sec (x) - 1 - tan^{2} (x) = 0

Rewrite using trig identities

sec (x) - 2 - sec^{2} (x) = 0

Solve by substitution

sec (x) = 1

sec (x) = 1 : x = 2 πn

Combine all the solutions

x = 2 πn

x, - sin (x y) y = 0

\frac{1}{cos ( x )} = \frac{5}{3}

6 cot (θ) + 5 = 0

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

cot (θ) = \frac{5}{7}

What is the general solution for sec(x)=sqrt(1-tan^2(x)) ?
The general solution for sec(x)=sqrt(1-tan^2(x)) is x=2pin