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

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

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

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

x = πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

sec^{2} (x)

from both sides

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

4 cosh (2 x) = 4 + sinh (2 x)

∣ sin (x) ∣ = sin (x) + 2

sin (a) = 0.2315

\frac{1 ( cos ^{2} ( x ) )}{( 1 - sin ^{2} ( x ) )} = 0

sin (x) sin^{3} (x) - sin^{5} (x) sin^{3} (x) = 0

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