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

The general solution for 2cot(x)+csc^2(x)=0 is x=(3pi)/4+pin

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = - 1

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn

2 cos^{2} (θ) + 3 cos (θ) + 4 = 3

2 sin (3 θ) cos (2 θ) - cos (2 θ) = 0

2 sec (x) + 1 = sec (x) + 3

sin (3 0^{\circ}) = cos (x - 2 0^{\circ})

- 7 sin (x) = 0

What is the general solution for 2cot(x)+csc^2(x)=0 ?
The general solution for 2cot(x)+csc^2(x)=0 is x=(3pi)/4+pin