IMO Shortlist 1969 problem 29
Dodao/la:
arhiva2. travnja 2012. ![(GDR 1)](/media/m/6/f/e/6fe33e9ed07886d04847853530f21b69.png)
Find all real numbers
![\lambda](/media/m/9/b/e/9be7eeb58b67ec913359062c0122ee80.png)
such that the equation
![(a)](/media/m/a/7/f/a7fedf50ce0b917a00dd07d5233906f1.png)
has no solution,
![(b)](/media/m/9/2/7/92773ef234467079b4efc86655fdc459.png)
has exactly one solution,
![(c)](/media/m/f/1/7/f17cafda3d149c9263bc72286e0f6dd3.png)
has exactly two solutions,
![(d)](/media/m/4/4/9/449877f09a0ebdf5fc68562d02511760.png)
has more than two solutions (in the interval
%V0
$(GDR 1)$ Find all real numbers $\lambda$ such that the equation $\sin^4 x - \cos^4 x = \lambda(\tan^4 x - \cot^4 x)$
$(a)$ has no solution,
$(b)$ has exactly one solution,
$(c)$ has exactly two solutions,
$(d)$ has more than two solutions (in the interval $(0, \frac{\pi}{4}).$
Izvor: Međunarodna matematička olimpijada, shortlist 1969