Solve the equation for 𝜃 if 0° ≤ 𝜃 < 360°. (Enter your answers as a comma-separated list.) 3 sec 𝜃 − 2 tan 𝜃 = 0

Answer 1

3secx - 2tanx = 0, secx=1/cosx, tanx = sinx/cosx

3/cosx - 2sinx/cosx = 0 multiply by cosx to eliminate the fraction

3 -2sinx = 0

sinx = 3/2 which is impossible as sines are never greater than 1

that's one method, converting everything to sines and cosines.

Or try it with tangents

3secx = 2tanx

3sec^2 - 2tanx = 0

1+ tan^2x = sec^2x

3(1+tan^2x) = 2tanx

3 +3tan^2x = 2tanx

3tan^2x - 2tanx +3 = 0

the discriminant = b^2 -4ac = 4-35 <0

there are no real solutions