Prove analytically that`(A-B)cupB=AcupB`

Prove analytically that (A-B)cup(B-A)=(AcupB)-(AcapB)

Prove analytically that A-B=AcapB^c

For any set A and B prove that : (A-B)uuB=AuuB .

What are beats?Show analytically how they are produced due to superposition of two sound waves.

Prove that tan(A+B)/cot(A-B)=(tan^2A-tan^2B)/(1-tan^2Atan^2B)

Show analytically how stationary wave are they formed due to superposition of two waves.

Verify with numerical examples and Venn diagram: Acup(BcupC)=(AcupB)cupC

A = {1, 2, 3}, B= {2, 3, 4}, C= {3, 4, 5} and U = {1,2, 3, 4, 5,6}. Verify the identities: Acup(BcapC)=(AcupB)cap(AcupC)

A = {1, 2, 3}, B= {2, 3, 4}, C= {3, 4, 5} and U= {1,2, 3, 4, 5,6}. Verify the identities: (AcupB)^c=A^c capB^c

Prove that (sin A+sin B)/(cos A+cos B)=tan((A+B)/2)