Question

\[solve ~for ~~~~0 \le x \le 2x\]\[5\cot x +2 +2\cot^2x=5\]

Answer 1

2cot^2(x)+5cot(x)-3=0
(2cotx-1)(cotx+3)=0

cotx=1/2, cotx=-3
tanx=2, tanx=-1/3

x=63.4, 243.4,161.6, 341.6 (Degrees)
x=1.11, 4.249, 2.821, 5.963 (Radians)

Answer 2

x=63.4, 243.4,161.6, 341.6 (Degrees)
x=1.11, 4.249, 2.821, 5.963 (Radians)

How did you get this? In both degrees and radians?

Answer 3

click you calculator \[x=\tan^{-1} 2 \]
For that x value, because the value "2" is positive (just look at the positive region), look at the thing that i draw for "tangent"

So,just now the value for \[x=\tan^{-1} 2 \]
x=63.43, then use that 180+63.43= 243.43 and get the "next" x value

so, you got
x=63.43, 243.43