Question

How do you solve `2 cos2(alpha)tan(alpha) + cos2(alpha) = 0`?

Answer 1

`(pi/4); (3pi)/4, 153^@43; 353^@43`

Explanation:

2cos 2x.tan x + cos 2x = 0
cos 2x(2tan x + 1) = 0
Trig unit circle and trig table -->
a. cos 2x = 0 --> `2x = pi/2` and `2x = (3pi)/2`
`2x = pi/2 --> x = pi/4`
`2x = (3pi)/2 --> x = (3pi)/4`
b. 2tan x + 1 = 0
`tan x = - 1/2`
Calculator and trig unit circle -->
`tan x = - 1/2` --> `x = - 26^@57` and `x = 180 - 26.57 = 153^@43`
Answers for (0, 2pi):
`pi/4; (3pi)/4 , 153^@43, and 333^@43` (or -26.57)