What is the general solution for sin^2(x)cot(x)-cot(x)=0 ?

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Factor

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

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

Solving each part separately

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

cot (x) = 0 : x = \frac{π}{2} + πn

sin (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

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

Combine all the solutions

x = \frac{π}{2} + πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Merge Overlapping Intervals

x = \frac{π}{2} + πn

x, cos (2 x) + sin (x) = 0

sin (x) = \frac{- 1}{3}

cos (\frac{x}{4}) = \frac{1}{2}

cos (2 x) = 5 cos (x) - 3

4 tan (A) = 2 tan (A) - 2

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