What is the general solution for 2csc^2(x)+5cot(x)=5 ?

The general solution for 2csc^2(x)+5cot(x)=5 is x=1.10714…+pin,x=2.81984…+pin

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2csc^2(x)+5cot(x)=5

2 csc^{2} (x) + 5 cot (x) = 5

x = 1.10714 \dots + πn, x = 2.81984 \dots + πn

Solution steps

2 csc^{2} (x) + 5 cot (x) = 5

Subtract

5

from both sides

2 csc^{2} (x) + 5 cot (x) - 5 = 0

Rewrite using trig identities

- 3 + 2 cot^{2} (x) + 5 cot (x) = 0

Solve by substitution

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

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

cot (x) = - 3 : x = arccot (- 3) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 2.81984 \dots + πn

60 sin (4 5^{\circ}) = 400 sin (θ)

(1 + tan (x)) (5 sin (x) - 2) = 0

arccos (e - x) = π^{3}

sin (a) = \frac{20}{25}

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

What is the general solution for 2csc^2(x)+5cot(x)=5 ?
The general solution for 2csc^2(x)+5cot(x)=5 is x=1.10714…+pin,x=2.81984…+pin