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

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

cot^{2} (x)

from both sides

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

Factor

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

cot^{2} (x) (cos (x) - 1) = 0

Solving each part separately

cot^{2} (x) = 0 or cos (x) - 1 = 0

cot^{2} (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

4 sin^{2} (θ) - 8 cos (θ) + 1 = 0, 0 \leq θ < 2 π

4 sin (A) + 3 = 2 sin (A) + 4

0 = - 18 cos (3 x)

cos^{2} (2 x) - 3 cos (2 x) = 0

csc^{2} (x) = sin (x)

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