Use an addition or subtraction formula to find the exact value of tan(285)

Question

anonymous · Answer

Cant you type this in your calculator?

anonymous · Answer

Tan(285) according to my Calc is -1.221

dumbcow · Answer

not for exact value....calc gives a decimal approximation

anonymous · Answer

Yes very true.

anonymous · Answer

It needs to be in exact terms, i.e. sqrt(3)/2, sqrt(2)/2 etc.

This is what I have so far:

$$(-1 - \sqrt{3}/3)/1 - \sqrt{3}/3$$

dumbcow · Answer

|dw:1383076821142:dw|
$$\tan(285) = \tan(105) = \tan(60+45)$$
$$\tan(a+b) = \frac{\tan a + \tan b}{1-\tan a \tan b}$$

anonymous · Answer

Ah I was doing tan(315 - 30) which might've been more complicated than 60 - 45

dumbcow · Answer

possibly, that will still work finding tan(315) on unit circle is just as easy

anonymous · Answer

I have sqrt{3} + 1 / 1 - sqrt{3}, where do I go from there?

dumbcow · Answer

multiply top/bottom by conjugate (1+sqrt3)

dumbcow · Answer

$$= \frac{4+2\sqrt{3}}{-2} = -2 - \sqrt{3}$$