Question
Solve the equation for x in the interval 0<x<2pi
1/ 1+tan^2x = -cos x
How would i do this? im thinking of maybe changing the 1+tan to sec^2x?
1/ 1+tan^2x = -cos x
How would i do this? im thinking of maybe changing the 1+tan to sec^2x?
Answers
drwls
Good idea. Use 1+tan^2 x = sec^2x
Then
1/(1+tan^2x) = -cos x
becomes
1/sec^2x = -cosx
cos^2x + cosx = 0
cosx (cosx + 1) = 0
cos x = 0 or -1
x = pi/2, 3 pi/2 or pi
Then
1/(1+tan^2x) = -cos x
becomes
1/sec^2x = -cosx
cos^2x + cosx = 0
cosx (cosx + 1) = 0
cos x = 0 or -1
x = pi/2, 3 pi/2 or pi