Question

Show that:

sin^2(45 + A) + sin^2(45 - A ) = 1

Answer 1

You can expand both binomials, and watch things cancel out, or note that

2sin^2(45+A) = 1-cos(90+2A)
2sin^2(45-A) = 1-cos(90-2A)

cos(90+x) = -sinx
cos(90-x) = sinx

Now just add it up.