TITLE: how **(1)** $(2n-1)\pi/2 + (-1)^n\pi/3$ and **(2)** $2n\pi±\pi/6$ indicates the same angle?
QUESTION [0 upvotes]: I'm learning Trigonometry right now with myself and at current about General solution. I have a question in my book which I don't understand how to proof. The question is Show that the two angles are indicated by the two following formulae - (1) $(2n-1)\pi/2 + (-1)^n\pi/3$ and (2) $2n\pi±\pi/6$ 
I don't know how to proof this, there is no trigonometry ratio given. Please help. Thankyou in advance.

REPLY [1 votes]: To simplify and work with integers, multiply all by $6/\pi$.
Then $3(2n-1)+2(-1)^n$ and $12n\pm1$ are $-1,1,11,13,23,25\cdots$ and $-1,1,11,13,23,25\cdots$.
Actually, the first formula reduces to the second with $2n,2n+1\leftrightarrow n$.
$$3(2\cdot2n-1)+2(-1)^{2n}=12n-3+2=12n-1,\\
3(2\cdot(2n+1)-1)+2(-1)^{2n+1}=12n+3-2=12n+1.$$
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