sec2ø-2tanø=4

Question

Solve the following equation for angles between 0 and 360 sec²Ø-2tanØ=4

Answer 1

 sec²Φ - 2tanΦ = 4

 

(1 + tan²Φ) - 2tanΦ = 4

 

tan²Φ - 2tanΦ - 3 = 0

 

(tanΦ - 3)(tanΦ + 1) = 0

 

tanΦ = 3 or tanΦ = -1

 

If tanΦ = 3, then Φ = tan^-13 = 71.6° or 180° + 71.6° = 251.6°

 

If tanΦ = -1, then Φ = 135° or 135° + 180° = 315°

 

Answer 2

sec² - 2 tan = 4

1 + tan² - 2 tan = 4      Pythagorean Identity

tan² - 2 tan - 3 = 0

 

Complete using zero product rule.