What is the general solution for (cos(x))/(sin(x))=0 ?

The general solution for (cos(x))/(sin(x))=0 is x= pi/2+pin

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(cos(x))/(sin(x))=0

\frac{cos ( x )}{sin ( x )} = 0

x = \frac{π}{2} + πn

Degrees

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

Solution steps

\frac{cos ( x )}{sin ( x )} = 0

Rewrite using trig identities

\frac{cos ( x )}{sin ( x )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (x)

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

sin (2 x) + 3 cos (2 x) = 0

7 cos (x) tan (x) - 5 tan (x) = 0

sec^{2} (x) - 6 sec (x) = 0

9 sec^{2} (x) tan (x) = 12 tan (x)

cos (x) = - \frac{4}{7}

What is the general solution for (cos(x))/(sin(x))=0 ?
The general solution for (cos(x))/(sin(x))=0 is x= pi/2+pin