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

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

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

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

x = \frac{π}{4} + πn, x = πn

Solution steps

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

Subtract

tan (x) + 1

from both sides

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

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

- \frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

8 (cos (x))^{2} - 6 sin (x) = 3

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

2 sin (3 θ) - 1 = 0, 0 \leq θ \leq 2 π

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