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

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

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cot(x)cos(x)-cot(x)=0

cot (x) cos (x) - cot (x) = 0

x = \frac{π}{2} + πn

Solution steps

cot (x) cos (x) - cot (x) = 0

Factor

cot (x) cos (x) - cot (x) : cot (x) (cos (x) - 1)

cot (x) (cos (x) - 1) = 0

Solving each part separately

cot (x) = 0 or cos (x) - 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = \frac{π}{2} + πn, x = 2 πn

Since the equation is undefined for:

2 πn

x = \frac{π}{2} + πn

sec^{2} (θ) - 25 = 0

cos (6 x) = - 1

cos (a) = - \frac{3}{2}

8 sin (2 x) = 8 cos (x)

cos (t) = \frac{2}{2}

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