how do i evaluate using formulas? i did almost the entire thing, but i can't finish the problem because i don't know how to simplify it:

tan(-5/12pi)

i can get until this part:

= (-6pi/24)+(4pi/24) / 1-(-2pi/24)

1 answer

sometimes it helps to "think" in degrees rather than radians, and then switch back.

e.g. (5/12)π = 75 degrees
so you want tan (-75)
You should know that tan(-A) = -tanA
so tan(-75)
= -tan75
= -tan(45+30)
= -(tan45 + tan30)/)1 - tan45tan30
= -(1 + 1/√3)/(1 - 1/√3)

multiply top and bottom by √3
= -(√3 + 1)/(√3 - 1)

so tan((-5/12)π) = -(√3+1)/(√3-1)
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