I a making an ex: and see this: tan x = -1 - tan x (pi/4) Why is the - before tan?

Question

I a making an ex: and see this: tan x = -1 <=> - tan x (pi/4) Why is the - before tan?

anonymous · Answer

for x?

anonymous · Answer

- tan x (pi/4) why is is not tan (-pi/4)

zehanz · Answer

It could just as well be tan (-pi/4), because tan is an uneven function: f(-x) = -f(x) for all x in the domain of f. I guess the reason -tan(pi/4) is used because you are supposed to know by heart that tan(pi/4) = 1. So we have: tan(x) = -1 <=> -tan(x) = 1 <=> tan(-x) = 1 <=> tan(-x) = tan(pi/4 + k*pi) <=> -x = pi/4 + k*pi <=> x = -pi/4 - k*pi which is the same as x = -pi/4 + k*pi, because k is any integer. Hope this helps... ZeHanz