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#