Question

2sin^2(45°-A) = 1-sin^2A

Answer 1

Manipulating left side:

2sin%5E2%2845-A%29

since sin%2845-A%29=+%28sqrt%282%29%2F2%29cos%28A%29-%28sqrt%282%29%2F2%29sin%28A%29, we have

=2%28%28sqrt%282%29%2F2%29cos%28A%29-%28sqrt%282%29%2F2%29sin%28A%29%29%5E2...simplify, factor out %281%2F2%29%5E2=1%2F4

=2%281%2F4%29%28sqrt%282%29cos%28A%29-sqrt%282%29sin%28A%29%29%5E2...simplify, factor out %28sqrt%282%29%29%5E2=2