Question

How do you solve `7cotx-sqrt3=4cotx` for `0<=x<=2pi`?

Answer 1

The Soln. Set. `={pi/3, 4pi/3} sub [0,2pi]`.

Explanation:

`7cotx-sqrt3=4cotx rArr 3cotx=sqrt3 rArr cotx=1/sqrt3`.

`rArr tanx=sqrt3=tan(pi/3)`

`:. x=pi/3` is a soln.

Now, the Principal Period of `tan` function is `pi`, i.e., to say,

`tantheta=tan(theta+pi)`, so, `pi/3+pi=4pi/3` is also soln.

So, the Soln. Set. `={pi/3, 4pi/3} sub [0,2pi]`.