What is the general solution for -6csc^2(x)+10cot(x)=-10 ?

The general solution for -6csc^2(x)+10cot(x)=-10 is x=1.89254…+pin,x=0.46364…+pin

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-6csc^2(x)+10cot(x)=-10

- 6 csc^{2} (x) + 10 cot (x) = - 10

x = 1.89254 \dots + πn, x = 0.46364 \dots + πn

Solution steps

- 6 csc^{2} (x) + 10 cot (x) = - 10

Subtract

- 10

from both sides

- 6 csc^{2} (x) + 10 cot (x) + 10 = 0

Rewrite using trig identities

4 + 10 cot (x) - 6 cot^{2} (x) = 0

Solve by substitution

cot (x) = - \frac{1}{3}, cot (x) = 2

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

cot (x) = 2 : x = arccot (2) + πn

Combine all the solutions

x = arccot (- \frac{1}{3}) + πn, x = arccot (2) + πn

Show solutions in decimal form

x = 1.89254 \dots + πn, x = 0.46364 \dots + πn

x, cos (x) - cos (y) = 0

- 3 tan^{2} (θ) + 2 tan (θ) = 6 tan (θ) + 1

sin (x) + cos (x) = - 3

sin (x) = \frac{1}{2}, cos (x) = - \frac{3}{2}

cos (x) = \frac{2 5}{5}

What is the general solution for -6csc^2(x)+10cot(x)=-10 ?
The general solution for -6csc^2(x)+10cot(x)=-10 is x=1.89254…+pin,x=0.46364…+pin