What is the general solution for 0=-6csc(x)cot(x) ?

The general solution for 0=-6csc(x)cot(x) is x= pi/2+pin

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0=-6csc(x)cot(x)

0 = - 6 csc (x) cot (x)

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

0 = - 6 csc (x) cot (x)

Switch sides

- 6 csc (x) cot (x) = 0

Solving each part separately

csc (x) = 0 or cot (x) = 0

csc (x) = 0 :

No Solution

csc (x) = 0

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

No Solution

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

General solutions for

cot (x) = 0

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{2} + πn

0.08 = 0.12 cos^{2} (3.922 t)

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

2 cos (3 θ) - 1 = 0

cos (4 x) = cos (8 x)

What is the general solution for 0=-6csc(x)cot(x) ?
The general solution for 0=-6csc(x)cot(x) is x= pi/2+pin