How do you simplify $tan(pi+theta)$ ?

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Answer 1 · 2017-02-24T21:17:57

$tan(pi+theta) = tan theta$

I don't know the tan addition formulae of the top, so I'd go with the sine/cosine ones:

$tan(pi+theta)$

$=( sin(pi+theta) )/ (cos(pi+theta) )$

$=( sin pi cos theta + sin theta cos pi) / (cos pi cos theta - sin pi sin theta )$

Here we remember that $cos pi = -1, sin pi = 0$

$implies( - sin theta ) / (- cos theta ) = tan theta$

Answer 2 · 2017-02-24T21:24:33

$tan theta$

Using the sum identity: $tan(pi+theta) = (tan pi + tan theta)/(1-tan pi* tan theta)$

$tan(pi) = (sin pi)/(cos pi) = 0/-1 = 0$

Therefore: $tan(pi+theta) = (0+tan theta)/(1-0) = tan theta$

How do you simplify tan(pi+theta)tan(pi+theta)?