Ineed with my math homework. the questions is: find all solutions of the equation in the interval [0,2π).
√3 tan(x- π/8)-1=0

and

Step-by-step explanation:

Let's first isolate the trig function.

Add 1 one on both sides:

Divide both sides by :

Now recall .

or

The first ratio I have can be found using in the first rotation of the unit circle.

The second ratio I have can be found using you can see this is on the same line as the so you could write as .

So this means the following:

is true when

where is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

Add on both sides:

Find common denominator between the first two terms on the right.

That is 24.

(So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval .

So if and we let , then solving for gives us:

( I just added on both sides.)

So recall .

Then .

Subtract on both sides:

Simplify:

So we want to find solutions to:

with the condition:

That's just at and

So now adding to both gives us the solutions to:

in the interval:

.

The solutions we are looking for are:

and

Let's simplifying:

and

and

and