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

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Question 1138387: Find tan((3pi/4)+theta) when tan theta = -1/2 .
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find

tan%28%283pi%2F4%29%2Btheta%29 when tan theta+=+-1%2F2 .
= tan%283pi%2F4-1%2F2%29
= tan%283pi%2F4-2%2F4%29
= tan%28%283pi-2%29%2F4%29
=tan%281.8562%29
=-3.408

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Apply the formula for tangent of the sum of arguments


    tan(a + b) = %28tan%28a%29%2Btan%28b%29%29%2F%281-tan%28a%29%2Atan%28b%29%29,


which is valid for all values of "a" and "b", where the tangent function is defined.


In your case,  a = 3pi%2F4%29,  b = theta,  and  tan%283pi%2F4%29 = -1,  so


    tan%283pi%2F4%2B+theta%29 = %28tan%283pi%2F4%29%2Btan%28theta%29%29%2F%281-tan%283pi%2F4%29%2Atan%28theta%29%29 = %28%28-1%29%2Btan%28theta%29%29%2F%281-%28-1%29%2Atan%28theta%29%29 = %28-1%2Btan%28theta%29%29%2F%281%2Btan%28theta%29%29 = 


        now substitute tan%28theta%29 = -1%2F2 to get


    tan%283pi%2F4%2B+theta%29 = %28-1+-+%28-1%2F2%29%29%2F%281%2B+%28-1%2F2%29%29 = %28%28-3%2F2%29%29%2F%28%281%2F2%29%29 = -3.      ANSWER

Solved.

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