What is the general solution for cot^4(x)=cot^4(x)sin(x) ?

The general solution for cot^4(x)=cot^4(x)sin(x) is x= pi/2+pin

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cot^4(x)=cot^4(x)sin(x)

cot^{4} (x) = cot^{4} (x) sin (x)

x = \frac{π}{2} + πn

Solution steps

cot^{4} (x) = cot^{4} (x) sin (x)

Subtract

cot^{4} (x) sin (x)

from both sides

cot^{4} (x) - cot^{4} (x) sin (x) = 0

Factor

cot^{4} (x) - cot^{4} (x) sin (x) : - cot^{4} (x) (sin (x) - 1)

- cot^{4} (x) (sin (x) - 1) = 0

Solving each part separately

cot^{4} (x) = 0 or sin (x) - 1 = 0

cot^{4} (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 - csc^{2} (x) = 0

tan (x) = \frac{- 3}{3}

2 arctanh (\frac{x - 2}{x + 1}) = ln (2)

sec (β) = 3, \frac{3 π}{2} < β < 2 π

cos (x) = \frac{2.9}{3.2}

What is the general solution for cot^4(x)=cot^4(x)sin(x) ?
The general solution for cot^4(x)=cot^4(x)sin(x) is x= pi/2+pin