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

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

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sec(x)tan(x)=0

sec (x) tan (x) = 0

x = πn

Degrees

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

Solution steps

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

2 cos (x) + 1 = 3

sec (x) + tan (x) = 0

sin (x + \frac{π}{6}) - sin (x - \frac{7 π}{6}) = \frac{3}{2}

3 cos^{2} (x) = sin^{2} (x)

sin (2 x) + sin (x) = 0, 0 \leq x \leq 2 π

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