Question 971377: Find all solutions of each equation on the interval(0, 2pi)
Sec^2 x + 2tan x = 0
Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628)   (Show Source):
Answer by ikleyn(53853)  (Show Source):
You can put this solution on YOUR website! .
Find all solutions of each equation on the interval (0, 2pi)
Sec^2 x + 2tan x = 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The solution in the post by @lwsshak3 is incorrect (incomplete).
He provided only one root of the equation in his answer, and gave incorrect value for it.
while the problem has two roots. So, one root was determined incorrectly, while the second root was missed.
I came to bring a correct solution.
sec^2 x + 2tan x = 0
lcd: cos^2(x)
1 + 2sin(x)*cos(x) = 0
1 + sin(2x) = 0
sin(2x) = -1
2x =  , k = 0, +/-1, +/-2, . . .
We take only two values 2x =  (k=0) and 2x =  (k=1),
since other values produce values of x out of the given interval.
ANSWER. The given equation has two roots in the interval [ , ).
They are  , or 135 degrees, and  , or 315 degrees.
Solved correctly.
|
|
|
