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

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

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cot^2(x)sin(x)=cot^2(x)

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

cot^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

cot^{2} (x) = 0 : x = \frac{π}{2} + πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

Merge Overlapping Intervals

x = \frac{π}{2} + πn

2 cos^{2} (w) + cos (w) - 3 = 0

csc (2 x) = \frac{3}{2}

sin (\frac{θ}{4}) = \frac{1}{2}

4 e^{c o s (x)} = 3

- 2 sin (B) - 6 = sin (B) - 3

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