I basically said something along the lines of "Tan(t) is the slope of a ray. Adding 2pi will create an angle with a terminal ray in the same spot as t. Thus t and (t+2pi) have the same slope and the same tangent."
If you want to use an identity, you could use the fact that we know tangent's period is pi. Since 2pi is a multiple of pi, tan(t)=tan(t+2pi).
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I basically said something along the lines of "Tan(t) is the slope of a ray. Adding 2pi will create an angle with a terminal ray in the same spot as t. Thus t and (t+2pi) have the same slope and the same tangent."
If you want to use an identity, you could use the fact that we know tangent's period is pi. Since 2pi is a multiple of pi, tan(t)=tan(t+2pi).
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