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

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

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

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

x = πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

sec^{2} (x) - 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = πn, x = \frac{π}{4} + πn

5 cos (x) = - 2 sin^{2} (x) + 4, 0 \leq x < 2 π

tan (x) = \frac{4 3}{4}

\frac{sin ^{2} ( x )}{1 - cos ( x )} = 1.23

x, 3 y = tan (6 x)

3 cos (x) = sec (x)

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