What is the general solution for (cot(x)-sqrt(3))(csc(x)+2)=0 ?

The general solution for (cot(x)-sqrt(3))(csc(x)+2)=0 is x= pi/6+pin,x=(11pi)/6+2pin

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(cot(x)-sqrt(3))(csc(x)+2)=0

(cot (x) - 3) (csc (x) + 2) = 0

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

Solution steps

(cot (x) - 3) (csc (x) + 2) = 0

Solving each part separately

cot (x) - 3 = 0 or csc (x) + 2 = 0

cot (x) - 3 = 0 : x = \frac{π}{6} + πn

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

Combine all the solutions

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

Merge Overlapping Intervals

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

sin (x) = \frac{7}{9.4}

cos (x) = \frac{6}{11}

3 cos^{2} (x) + 5 sin (x) - 1 = 0

2 cos^{2} (θ) = 7 cos (θ) - 3

sin (θ) = (\frac{173}{210})

What is the general solution for (cot(x)-sqrt(3))(csc(x)+2)=0 ?
The general solution for (cot(x)-sqrt(3))(csc(x)+2)=0 is x= pi/6+pin,x=(11pi)/6+2pin