You can put this solution on YOUR website! Solve each equation for x in the interval 0≤x ≤2 π:
1/(1+tan²x) = -cosx
-----------------
Since sin^2 + cos^2 = 1
dividing by cos^2 you get
tan^2 + 1 = sec^2
----------------------
So your problem becomes
1/sec^2 = -cosx
cos^2 + cos = 0
cos(cos+1) = 0
cosx = 0 or cosx = -1
x = pi/2 or x = pi
=====================
Cheers,
Stan H.
(