Explain how respiration and photosynthesis are chemically opposite from each other

They are chemically opposite in that the reactants of one are the products of the other. One could not exist without the other to supply the materials. 

You can look up the reactants and products in any Biology textbook. also In Photosynthesis carbon dioxide and energy is consumed to give sugar and Oxygen. 
while in Respiration oxygen and sugar is consumed to give energy and carbon dioxide is produced. 

Hence the two are opposite of each other. 

Now, since you need oxygen to respire there must be a constant supply of oxygen and plants are the source of oxygen since they produce oxygen due to photosynthesis, similarly plants need oxygen to do photosynthesis which is produced by respiration. 

Hence they both are dependent on each other   HOPE IT HELP ;D