Step 1: Identity ( \sec^2 x = 1 + \tan^2 x ). ( 1 + \tan^2 x - 2\tan x = 0 ) ( \tan^2 x - 2\tan x + 1 = 0 ) ( (\tan x - 1)^2 = 0 ) ⇒ ( \tan x = 1 ).
Guía Completa de Ecuaciones Trigonométricas: 1º Bachillerato (Ejercicios Resueltos) Step 1: Identity ( \sec^2 x = 1 + \tan^2 x )
Step 3: Union of solutions: ( 0,\ \frac\pi2,\ \pi,\ \frac3\pi2 ). Answer: Same as above. Step 1: Identity ( \sec^2 x = 1 + \tan^2 x )
Para (\tan x = -\sqrt3): [ x = 120^\circ = \frac2\pi3 + k\pi ] Step 1: Identity ( \sec^2 x = 1 + \tan^2 x )
Step 1: Identity ( \sec^2 x = 1 + \tan^2 x ). ( 1 + \tan^2 x - 2\tan x = 0 ) ( \tan^2 x - 2\tan x + 1 = 0 ) ( (\tan x - 1)^2 = 0 ) ⇒ ( \tan x = 1 ).
Guía Completa de Ecuaciones Trigonométricas: 1º Bachillerato (Ejercicios Resueltos)
Step 3: Union of solutions: ( 0,\ \frac\pi2,\ \pi,\ \frac3\pi2 ). Answer: Same as above.
Para (\tan x = -\sqrt3): [ x = 120^\circ = \frac2\pi3 + k\pi ]