Question

How do you use a half-angle formula to simplify `tan(292.5)`?

Answer 1

Simplify tan (292.5)

Explanation:

Call x = tan 292.5
tan = 2(292.5) = tan 585 = (135 + 360) = tan (135) = - tan (45) = - 1

Use trig identity:`tan 2x = (2tan x)/(1 - tan^2 x)`

`- 1 = (2x)/(1 - x^2)` -> `x^2 - 2x - 1 = 0`

`D = d^3 = 4 + 4 = 8 -> d = +- 2sqrt2`

`tan (292.5) = x = 1 - (sqrt2)` (Quadrant IV)