Question

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

Answer 1

Hello Friend,

Here's the answer.

Hope it helps.

Purva
@Purvaparmar1405
Brainly.in

Answer 2

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