What is the general solution for cot(x)cos^2(x)=cot(x) ?

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

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cot(x)cos^2(x)=cot(x)

cot (x) cos^{2} (x) = cot (x)

x = \frac{π}{2} + πn

Solution steps

cot (x) cos^{2} (x) = cot (x)

Subtract

cot (x)

from both sides

cos^{2} (x) cot (x) - cot (x) = 0

Factor

cos^{2} (x) cot (x) - cot (x) : cot (x) (cos (x) + 1) (cos (x) - 1)

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

Solving each part separately

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

cot (x) = 0 : x = \frac{π}{2} + πn

cos (x) + 1 = 0 : x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = \frac{π}{2} + πn, x = π + 2 πn, x = 2 πn

Since the equation is undefined for:

π + 2 πn, 2 πn

x = \frac{π}{2} + πn

2 sin (2 x) + 5 = 4

x, sin (x) = cos (x)

sin (θ) = - \frac{3}{2}, 0 \leq θ \leq 2 π

sin (x) + cos (x) = \frac{1}{2}

cot (x) = 4

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