Question

Solve the equation sin2 x + 3cos2 x = 0 for 0 ◦ ≤ x ≤ 360 ◦ .

Answer 1

sin2x + 3cos2x = 0 for 0 ≤ x ≤ 2π

sin2x = -3cos2x

sin2x / cos2x = -3

Recall : Trigonometry identities tan2x = sin2x / cos2x

tan2x = -3

Recall : Trigonometry identities tan2x = 2tanx / (1 - tan²x)

2tanx / (1 - tan²x) = -3

2tanx = -3(1 - tan²x) = -3 + 3tan²x

3tan²x - 2tanx - 3 = 0

This is a quadratic equation for tanx

Substitute a = 3 , b = -2 and c = -3

There fore tanx = (- b ± √b² - 4ac) / 2a

tanx = (2 ± √4 - 4(3)(-3) ) / 2(3) = (2 ±√4 + 36) / 6

tanx = (1 ± √10) / 3

x = tan^-1[(1 ± √10) / 3].