What is the general solution for -8csc^2(x)-4cot(x)=-12 ?

The general solution for -8csc^2(x)-4cot(x)=-12 is x=(3pi)/4+pin,x=1.10714…+pin

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-8csc^2(x)-4cot(x)=-12

- 8 csc^{2} (x) - 4 cot (x) = - 12

x = \frac{3 π}{4} + πn, x = 1.10714 \dots + πn

Solution steps

- 8 csc^{2} (x) - 4 cot (x) = - 12

Subtract

- 12

from both sides

- 8 csc^{2} (x) - 4 cot (x) + 12 = 0

Rewrite using trig identities

4 - 4 cot (x) - 8 cot^{2} (x) = 0

Solve by substitution

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

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

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

Combine all the solutions

x = \frac{3 π}{4} + πn, x = arccot (\frac{1}{2}) + πn

Show solutions in decimal form

x = \frac{3 π}{4} + πn, x = 1.10714 \dots + πn

2 cos (2 x) + 43 sin (x) = 5

sin (2 x) + 2 cos^{2} (x) = 0

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

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

cos (x) = 0, 0 \leq x < 2 π

What is the general solution for -8csc^2(x)-4cot(x)=-12 ?
The general solution for -8csc^2(x)-4cot(x)=-12 is x=(3pi)/4+pin,x=1.10714…+pin