SOLUTION: Find Tan(3pi/4+theta) when tan theta= 1/2

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Question 957305: Find Tan(3pi/4+theta) when tan theta= 1/2
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The formula to use is 

tan%28alpha%2Bbeta%29%22%22=%22%22%28tan%28alpha%29%2Btan%28beta%29%29%2F%281-tan%28alpha%29tan%28beta%29%29

tan%283pi%2F4%2Btheta%29 when tan%28theta%29%22%22=%22%221%2F2

We substitute 

alpha%22%22=%22%223pi%2F4

and so we substitute

tan%283pi%2F4%29%22%22=%22%22-1

and we are given:

tan%28theta%29%22%22=%22%221%2F2

Substituting in

tan%28alpha%2Bbeta%29%22%22=%22%22%28tan%28alpha%29%2Btan%28beta%29%29%2F%281-tan%28alpha%29tan%28beta%29%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22%28tan%283pi%2F4%29%2Btan%28theta%29%29%2F%281-tan%283pi%2F4%29tan%28theta%29%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22%28-1%2B1%2F2%29%29%2F%281-%28-1%29%281%2F2%29%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22%28-1%2F2%29%29%2F%281%2B1%2F2%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22%28-1%2F2%29%29%2F%282%2F2%2B1%2F2%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22%28-1%2F2%29%29%2F%283%2F2%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22%28-1%2F2%29%29%2A%282%2F3%29

tan%283pi%2F4%2Btheta%29%22%22=%22%22-1%2F3

Edwin