Question

(sina+cosa)^2+(sina-cosa)^2-2

Answer 1

Sin^2a+2sinacosa+cos^2a+sin^2a-2cosasina+cos^2a-2=2sin^2+2cos^2-2=
=2(sin^2a+cos^2a)-2=2-2=0

Answer 2

We can simplify the expression using the identities: (a + b)^2 = a^2 + 2ab + b^2 (a - b)^2 = a^2 - 2ab + b^2

Let a = sina and b = cosa, then we have:

(sina + cosa)^2 + (sina - cosa)^2 - 2 = sina^2 + 2sina cosa + cosa^2 + sina^2 - 2sina cosa + cosa^2 - 2 (using the identities above) = 2sina^2 + 2cosa^2 - 2 = 2(sin^2(a) + cos^2(a)) - 2 = 0

Therefore, the expression simplifies to 0.