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

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Factor

cot (x) sin (x) + cot (x) : cot (x) (sin (x) + 1)

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

Solving each part separately

cot (x) = 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

Combine all the solutions

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

Merge Overlapping Intervals

x = \frac{π}{2} + πn

4 cos (2 θ) = 4 sin (2 θ)

tan (x) = - 3, 0 \leq x \leq 2 π

5 tan^{2} (A) - 7 = 8

tan (x) = \frac{28}{16}

2 sin^{2} (x) = 3 - sin (x)

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