Crest and Trough Interference - Light Wave Explanation

[HUMERA.S]

when light waves interfere, it is said that when the troughs of both the waves (say) coincide, destructive interference takes place. it means that the waves have min. energy at crest and max. at crest. i don't understand how this could be, following that both(crest and trough) have the same amplitude and are at equal displacements of the wave !
would someone please clarify this...

 

[Zubeen]

waves have min. energy at crest and max. at crest. i don't ...

you have mistaken here it must be minimum at trough and maximum at crests.
Well, you are right in saying that they have the same amplitude
but what here matters is the sign they have i.e. at troughs the amplitude is in negative direction while in crests its in positive.
And its usually mistaken that the graph representing a way shows displacement of something but its not so , the graph shows the amplitude of energy (for any type of wave) at that point.