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To play a cross court net shot you should try and approach the net as though you are going to play a straight net shot and just before impact get your racket outside the line of the shuttle to create the space and racket angle required to turn the shuttle cross-court.
For a forehand cross-court net shot, present the straight net with palm facing upwards.
Bring the racket head across the net out to in with a slight pulling action to move the shuttle cross court.
For the backhand net, the approach will be with backhand grip and flat face, with thumb underneath.
Here the cross net is created through a slight pulling action from out to in on the backhand side of the court.