Question

Solve the multiple angle equation in the interval (0, 2ð) tan2x=-1
Do i have to divide the 2 to the other side?

Answer 1

I read you interval as (0 , 2π)

tan 2x = -1
I know tan 45° = tan π/4 = +1
for a negative tangent, the angle is in either II or Iv
so 2x = (180-45)° or 2x = (360-45)°
2x = 135° or 2x = 315° OR 2x = 3π/4 or 2x = 7π/4

x = 67.5° or x = 157.5° OR x = 3π/8 or x = 7π/8

but the period of tan 2x = 90° or π/2
so two more answers in your domain
x = 67.5 + 90 = 157.5 (already have that) or
x = 157.5 + 90 = 247.5°

in radians: x = 7π/8 + π/2 = 11π/8

so:
x = 67.5° , 157.5° , 247.5° OR x = 3π/8 , 7π/8 , 11π/8

Answer 2

Wow, that actually makes perfect sense, thank you!!!!