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

The general solution for sec^2(x)-1=tan(x) is x= pi/4+pin,x=pin

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

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

x = \frac{π}{4} + πn, x = πn

Solution steps

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

Subtract

tan (x)

from both sides

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

Rewrite using trig identities

- tan (x) + tan^{2} (x) = 0

Solve by substitution

tan (x) = 1, tan (x) = 0

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 0 : x = πn

Combine all the solutions

x = \frac{π}{4} + πn, x = πn

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

2 sin (2 x) = cos (x)

(tan (θ) + 1) (sec (θ) - 2) = 0

sin (3 x) = 2 sin (x)

cot (θ) = - \frac{2}{3}

What is the general solution for sec^2(x)-1=tan(x) ?
The general solution for sec^2(x)-1=tan(x) is x= pi/4+pin,x=pin