# Inequalities (trig) + Attempted

tanx + 3cotx = 4

## The Attempt at a Solution

Heres my attempt:

tanx + 3/tanx - 4 = 0
(tan^2x -4tanx + 3) / tanx = 0

tan^2x - 4 tanx + 3

(tanx - 3 ) (tanx - 1 ) = 0

tan = 3, tan = 1

im not sure about tan = 3, but for tan = 1 , pi/4 +180n,
is this correct? if it is how would i go about findin solutions for tan=3.

thanks.

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rock.freak667
Homework Helper
The same way you solved tanx=1

tanx=3, the principle angle is tan-1(3)

how would we represent tan^-1(3) interms of radians ?
calculators are not allowed in our school, is there a way ?

rock.freak667
Homework Helper
how would we represent tan^-1(3) interms of radians ?
calculators are not allowed in our school, is there a way ?
Unfortunately there is not.

hmm..
so we just find solutions for tan = 1 ?

eumyang
Homework Helper
im not sure about tan = 3, but for tan = 1 , pi/4 +180n,
is this correct? if it is how would i go about findin solutions for tan=3.
"pi/4 +180n" -> Don't mix degree and radian measure. Also, state what "n" is. You should write
$$\frac{\pi}{4} + n \pi, n \in \mathbb{Z}$$

hmm..
so we just find solutions for tan = 1 ?
No, you still need both solutions. The other could be written as
$$\tan^{-1} 3 + n \pi, n \in \mathbb{Z}$$

tan^-1(3) + npi
how do you write that interms of pi?

i've never seen anything like that. could you please give me an example?

rock.freak667
Homework Helper
tan^-1(3) + npi
how do you write that interms of pi?

i've never seen anything like that. could you please give me an example?
you can't write tan-1(3) in terms of pi. That is why you have to leave it as is.

ok, just to make sure.. are my previous steps correct?
just to double check. thanks

rock.freak667
Homework Helper
ok, just to make sure.. are my previous steps correct?
just to double check. thanks
Yes they are correct.