Question 519724
First before checking out the answer just check out the RHS side of your question.

LHS=(5cos E - 2sin E)^2 + (2cos E +5 sin E)^2 
   =25cos^2E-20cosEsinE + 4sin^2E + 4cos^2E +20cosEsinE+25sin^2E
   =1+0+1 (using identity cos^2E+sin^2E=1)
   =2
   =RHS