Solve for all values of x between 0 degrees and 360 degrees.

Question

5tan ^2x-2 = 4 tanx?

Answer 1

5tan²x - 2 = 4tanx

Subtract 4tanx from each side

5tan²x - 4tanx - 2 = 0

This is a quadratic equation for tanx

tanx = [-b ± sqrt(b² - 4ac)] / 2a

Substitute a = 5 , b = -4 and c = -2 in the above tanx

tanx = [4 ±sqrt(16 -4(-10))] / 2(5)

tanx = [4 ± sqrt(56)] / 10

tanx = [4 ± 2sqrt(14)] / 10

x = tan^-1[[4 + 2sqrt(14)] / 10] and

x = tan^-1[[4 - 2sqrt(14)] / 10].