Question

3 sec^2x = 8 tanx - 2

Answer 1

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Answer 2

3 sec²x = 8 tan x - 2

Substitute Sec²x = tan² x + 1

3 sec²x = 8 tan x - 2

3(tan² x + 1) =  8 tan x - 2

3 tan²x + 3 =  8 tan x - 2

3 tan²x - 8 tan x + 5  = 0

Let k = tan x :

3k² - 8k + 5  = 0

(3k - 5) (k - 1) = 0

k = 5/3 or k = 1

When k = 5/3

tan x = 5/3

x = 59º

when k = 1

tan x = 1

x = 45º

Answer: x = 59º or x = 45º