What is the general solution for (cot(x)-1)(2sin(x)+1)=0 ?

The general solution for (cot(x)-1)(2sin(x)+1)=0 is x= pi/4+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

x = \frac{π}{4} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Solving each part separately

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

cot (x) - 1 = 0 : x = \frac{π}{4} + 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}{4} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

y, x = tan (y)

tan (x) = - \frac{12}{5}

2 cos (x) = sin (x)

cot (\frac{3 θ}{2}) = - 3

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

What is the general solution for (cot(x)-1)(2sin(x)+1)=0 ?
The general solution for (cot(x)-1)(2sin(x)+1)=0 is x= pi/4+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin