determine the least positive angle sin^2x+cos^2x+tan^2x=4/3?

sin²(x) + cos²(x) + tan²(x) = 4/3 → recall: sin²(x) + cos²(x) = 1

1 + tan²(x) = 4/3

tan²(x) = (4/3) - 1

tan²(x) = 1/3

tan²(x) = (± 1/√3)²

tan(x) = ± 1/√3

tan(x) = ± (√3)/3


First case: tan(x) = (√3)/3

x = π/6


Second case: tan(x) = - (√3)/3

x = - π/6

so cos ²x = 3 / 4====> cos x = ±√3 / 2 ===> for you π / 6