Question

if 3 sec^4 A + 8 = 10 sec^2 A, find the values of tan A​

Answer 1

Answer:

tanA = ±1/√3 and ±1

Step-by-step explanation:

3sec⁴A + 8 = 10sec²A

3(sec²A)² + 8 = 10sec²A

Let sec²A = P

3P² + 8 = 10P

3P² - 10P + 8 = 0

3P² -6P - 4P + 8 = 0

3P(P -2) -4(P -2) = 0

(3P -4) (P -2) = 0

P = 4/3 and 2

sec²A = 4/3 and 2

[ we know,

sec²x - tan²x = 1 use, this ]

1 + tan²A = 4/3

tan²A = 4/3 -1 = 1/3

tan²A = ± 1/√3

again,

sec²A = 2

1 + tan²A = 2

tan²A = 1

tan²A = tan²π/4

tanA = ± 1

hence, tanA = ±1/√3 and ±1