What is the general solution for csc(x)cot(x)+cot(x)=0 ?

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

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csc(x)cot(x)+cot(x)=0

csc (x) cot (x) + cot (x) = 0

x = \frac{π}{2} + πn

Solution steps

csc (x) cot (x) + cot (x) = 0

Factor

csc (x) cot (x) + cot (x) : cot (x) (csc (x) + 1)

cot (x) (csc (x) + 1) = 0

Solving each part separately

cot (x) = 0 or csc (x) + 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

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

Combine all the solutions

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

Merge Overlapping Intervals

x = \frac{π}{2} + πn

tan (x) = \frac{50}{36}

- 2 + cot (x) = - 3

θ, ρ = sin (φ) sin (θ)

3 cos^{2} (x) - 6 cos (x) = - 3, 0 \leq x \leq 2 π

csc (θ) + 2 = 0, 0 \leq θ \leq 2 π

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