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## Homework Statement

Is it possible to solve tan(x) = 3 without the use of a calculator?

The knowns:

1) It originaly came from trying to solve 1/(cos^2) -2tan = 4.

1 = cos^2+sin^2 so this can be converted into tan^2 -2tan-3 = 0 which solves for

tan = -1(easy) and tan = 3(?)

If there is another way to solve without tan=3 then it would be ok, but still more interesting if tanx = 3 can be solved.

2) All sin,cos,tan,cot for angles 0,30,45,60,90 and multiples.

3) Trigonometric circle

All else has to be proved.

## Homework Equations

## The Attempt at a Solution

I tried using the trigonometric circle, but I couldn't find any useful relation. Tried squaring, nothing happens. Tried converting to sin and cos, nothing. I know the solution is 2pi/5 but can't find a way to bring it up to the rhs of the equation.

I just thing that the textbook is juts wrong to ask that with this kind of information.