What is the general solution for csc^2(x)-4cot(x)=-2 ?

The general solution for csc^2(x)-4cot(x)=-2 is x=0.32175…+pin,x= pi/4+pin

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csc^2(x)-4cot(x)=-2

csc^{2} (x) - 4 cot (x) = - 2

x = 0.32175 \dots + πn, x = \frac{π}{4} + πn

Solution steps

csc^{2} (x) - 4 cot (x) = - 2

Subtract

- 2

from both sides

csc^{2} (x) - 4 cot (x) + 2 = 0

Rewrite using trig identities

3 + cot^{2} (x) - 4 cot (x) = 0

Solve by substitution

cot (x) = 3, cot (x) = 1

cot (x) = 3 : x = arccot (3) + πn

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = arccot (3) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = 0.32175 \dots + πn, x = \frac{π}{4} + πn

sin (2 x - \frac{π}{3}) = \frac{3}{2}

- sin^{3} (t) + sin (2 t) cos (t) = 0

tan (θ) = 3 tan (4 5^{\circ})

- cot (x) csc (x) = 0

2 cos (2 θ) - 3 cos (θ) - 5 = - 7

What is the general solution for csc^2(x)-4cot(x)=-2 ?
The general solution for csc^2(x)-4cot(x)=-2 is x=0.32175…+pin,x= pi/4+pin