What is the general solution for |tan(x)|=1 ?

The general solution for |tan(x)|=1 is x=(3pi)/4+pin,x= pi/4+pin

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|tan(x)|=1

∣ tan (x) ∣ = 1

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Solution steps

∣ tan (x) ∣ = 1

Solve by substitution

tan (x) = - 1 or tan (x) = 1

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

3 sin (x) + 4 = 5 cos (x)

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

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

2 cos (2 x) + 1 = 0, 0 \leq x \leq 2 π

sec (x) + tan (x) - 1 = 0

What is the general solution for |tan(x)|=1 ?
The general solution for |tan(x)|=1 is x=(3pi)/4+pin,x= pi/4+pin