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**Let S={x ∈ R; -π/2 < x < π/2 }**and let V be the subset of R2 given by V=S^2={(x,y); -

**π/2 < x <**

**π/2}, with vector addition ( (+) ).**For each (for every)

__u__∈**V**, For each (for every)

__v__**∈ V**with u=(x1 , y1) and v=(x2,y2)

__u__+__v__= (arctan (tan(x1)+tan(x2)), arctan (tan(y1)+tan(y2)) )**Note: The vectors are ordered pairs of real numbers between -π/2 and π/2, and we are using non-standard vector addition.**

Show that V with the designated operations forms a vector space.

Make sure that you show verification for EACH of the ten Vector Space Axioms.

My question is how would you apply the additive identity to prove that

My question is how would you apply the additive identity to prove that

__u__+__0__=__u__to show that V forms a vector space?