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

The general solution for 2cot(x)sin(x)+cot(x)=0 is x= pi/2+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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2cot(x)sin(x)+cot(x)=0

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

x = \frac{π}{2} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Factor

2 cot (x) sin (x) + cot (x) : cot (x) (2 sin (x) + 1)

cot (x) (2 sin (x) + 1) = 0

Solving each part separately

cot (x) = 0 or 2 sin (x) + 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

2 sin (x) + 1 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin (x) - (2 + 3) = - 3 csc (x)

7 cos^{2} (θ) + 6 sin (θ) - 10 = - 4

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

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

tan (θ) = \frac{7}{6}

What is the general solution for 2cot(x)sin(x)+cot(x)=0 ?
The general solution for 2cot(x)sin(x)+cot(x)=0 is x= pi/2+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin