tan (45+x) = tan (45-x). Solve for x.

Question

Grateful for any help. Pretty sure I'm supposed to use the compound angle formula so I tried it but then hit a dead end.

Answer 1

tan(45+x)=tan(45-x)

(tan45+tanx)/(1-tan45tanx)=(tan45-tanx)/(1+tan45tanx)

tan45=1

(1+tanx)/1-tanx)=(1-tanx)/(1+tanx)

cross multiply

(1+tanx)^2=(1-tanx)^2

1+2tanx+tan^2=1-2tanx+tan^2x

cancel 1 on both sides and cancel tan^2x on both sides

2tanx=-2tanx

4tanx=0

tanx=0

x=0° and x=180°

check: if x=0, then you get tan45=tan45, 1=1

if x=180 you get...

tan(225)=tan(-135), 1=1, ( you are at the same point on the unit circle)