What is the general solution for 8csc^2(x)-2cot(x)=9 ?

The general solution for 8csc^2(x)-2cot(x)=9 is x=1.10714…+pin,x=1.81577…+pin

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8csc^2(x)-2cot(x)=9

8 csc^{2} (x) - 2 cot (x) = 9

x = 1.10714 \dots + πn, x = 1.81577 \dots + πn

Solution steps

8 csc^{2} (x) - 2 cot (x) = 9

Subtract

9

from both sides

8 csc^{2} (x) - 2 cot (x) - 9 = 0

Rewrite using trig identities

- 1 - 2 cot (x) + 8 cot^{2} (x) = 0

Solve by substitution

cot (x) = \frac{1}{2}, cot (x) = - \frac{1}{4}

cot (x) = \frac{1}{2} : x = arccot (\frac{1}{2}) + πn

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

Combine all the solutions

x = arccot (\frac{1}{2}) + πn, x = arccot (- \frac{1}{4}) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 1.81577 \dots + πn

cos (d) = \frac{9}{15}

coth^{2} (x) + csch^{2} (x) = 2

tan (x) = \frac{3}{9}

2 cos (x) = 3 cot (x)

sin^{2} (x) + 2 sin (x) - 1 = 0

What is the general solution for 8csc^2(x)-2cot(x)=9 ?
The general solution for 8csc^2(x)-2cot(x)=9 is x=1.10714…+pin,x=1.81577…+pin