What is the general solution for 3csc^2(x)+1.5cot(x)=15 ?

The general solution for 3csc^2(x)+1.5cot(x)=15 is x=0.51534…+pin,x=2.72592…+pin

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3csc^2(x)+1.5cot(x)=15

3 csc^{2} (x) + 1.5 cot (x) = 15

x = 0.51534 \dots + πn, x = 2.72592 \dots + πn

Solution steps

3 csc^{2} (x) + 1.5 cot (x) = 15

Subtract

15

from both sides

3 csc^{2} (x) + 1.5 cot (x) - 15 = 0

Rewrite using trig identities

- 12 + 1.5 cot (x) + 3 cot^{2} (x) = 0

Solve by substitution

cot (x) = \frac{- 1 + 65}{4}, cot (x) = - \frac{1 + 65}{4}

cot (x) = \frac{- 1 + 65}{4} : x = arccot (\frac{- 1 + 65}{4}) + πn

cot (x) = - \frac{1 + 65}{4} : x = arccot (- \frac{1 + 65}{4}) + πn

Combine all the solutions

x = arccot (\frac{- 1 + 65}{4}) + πn, x = arccot (- \frac{1 + 65}{4}) + πn

Show solutions in decimal form

x = 0.51534 \dots + πn, x = 2.72592 \dots + πn

sin (y) = cos (y)

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

θ, 2 cos^{2} (θ) + 9 cos (θ) - 5 = 0

tan (3 x) = - 3, 0 \leq x \leq 2 π

5 cos (θ) = - 3

What is the general solution for 3csc^2(x)+1.5cot(x)=15 ?
The general solution for 3csc^2(x)+1.5cot(x)=15 is x=0.51534…+pin,x=2.72592…+pin