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

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

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1+cot^2(x)+2csc(x)=0

1 + cot^{2} (x) + 2 csc (x) = 0

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

Solution steps

1 + cot^{2} (x) + 2 csc (x) = 0

Rewrite using trig identities

csc^{2} (x) + 2 csc (x) = 0

Solve by substitution

csc (x) = 0, csc (x) = - 2

csc (x) = 0 :

No Solution

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

Combine all the solutions

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

4 sin (2 x) = 3 sin (x)

sin (a) = 0.1245

x, sin (x + z) = cos (y + z)

y, tan (y) = \frac{94}{152} c m

(sin (x) - 1) (sin (x) - 4) = 0

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