Originally posted by jay_rocks:
5tan x + 6 = 2 / cos^2 x
2cosec^2 x + cot x -8 =0
find angles btw (0>x>360)degree
i)5 tan x + 6 = 2 / cos^2 x
--> 5 tan x + 6 = 2 sec^2 x
---> 5 tan x + 6 = 2 (1 + tan^2 x)
--> 2 tan^2 x - 5 tan x - 4 = 0
Let y = tan x
--> 2y^2 - 5y - 4 = 0
....too lazy to think, you can continue on from there.
ii)2 cosec^2 x + cot x - 8 = 0
--> 2(1 + cot^2 x) + cot x - 8 = 0
--> 2 cot^2 x + cot x - 6 = 0
Let y = cot x
--> 2y^2 + y - 6 = 0
--> (2y - 3)(y + 2) = 0
--> y = 2/3 or y = -2
--> cot x = 2/3 or cot x = -2
Continue using calculator.