What is the general solution for (tan(x)-1)(sec(x)-1)=0 ?

The general solution for (tan(x)-1)(sec(x)-1)=0 is x= pi/4+pin,x=2pin

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

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

x = \frac{π}{4} + πn, x = 2 πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n, x = 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Solving each part separately

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

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

tan (x) - 1 = 0

Move

1

to the right side

tan (x) - 1 = 0

Add

1

to both sides

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

Simplify

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

sec (x) - 1 = 0 : x = 2 πn

sec (x) - 1 = 0