What is the general solution for -6csc^2(x)+cot(x)=-18 ?

The general solution for -6csc^2(x)+cot(x)=-18 is x=2.49809…+pin,x=0.58800…+pin

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-6csc^2(x)+cot(x)=-18

- 6 csc^{2} (x) + cot (x) = - 18

x = 2.49809 \dots + πn, x = 0.58800 \dots + πn

Solution steps

- 6 csc^{2} (x) + cot (x) = - 18

Subtract

- 18

from both sides

- 6 csc^{2} (x) + cot (x) + 18 = 0

Rewrite using trig identities

12 + cot (x) - 6 cot^{2} (x) = 0

Solve by substitution

cot (x) = - \frac{4}{3}, cot (x) = \frac{3}{2}

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

cot (x) = \frac{3}{2} : x = arccot (\frac{3}{2}) + πn

Combine all the solutions

x = arccot (- \frac{4}{3}) + πn, x = arccot (\frac{3}{2}) + πn

Show solutions in decimal form

x = 2.49809 \dots + πn, x = 0.58800 \dots + πn

tan (θ) = \frac{7}{7}

x, tan (x + y + \frac{π}{4}) = e^{y}

tan (2 x) = 0.75

3 tan^{2} (x) + 7 tan (x) + 4 = 0

cos (2 θ) - 3 = - 5 sin (θ)

What is the general solution for -6csc^2(x)+cot(x)=-18 ?
The general solution for -6csc^2(x)+cot(x)=-18 is x=2.49809…+pin,x=0.58800…+pin