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

The general solution for 0=sec(x)tan(x) is x=pin

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0=sec(x)tan(x)

0 = sec (x) tan (x)

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

0 = sec (x) tan (x)

Switch sides

sec (x) tan (x) = 0

Solving each part separately

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

sec (x) = 0 :

No Solution

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 0

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 = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

Combine all the solutions

x = πn

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

8 sin (x) + 12 = 16

cos (7 x) = - 1

8 sin (t) + 8 cos (t) = 8

5 sin (\frac{π}{3} x) = 2

What is the general solution for 0=sec(x)tan(x) ?
The general solution for 0=sec(x)tan(x) is x=pin