Question

why is sin^2(67.5˚) = (2√2+1)/(2√2) and not (2√2-1)/(2√2)?

my working:
sin^2(67.5˚)
=(cos2A)/2 +1
=[cos(67.5)]/2 +1
=(cos135)/2 +1
=(-1/√2)/2 +1
=(2√2-1)/(2√2)

could someone figure out what went wrong? ><

Answer 1

cos(2x)=1-2sin^2(x)
-1+cos(2x)=-2sin^2(x)
(1-cos(2x))/2=sin^2(x) <---------------- you did not divide the one
(1-cos(135)/2=sin^2(67.5)
(1+1/sqrt(2))/2=sin^2(67.5)
(1+sqrt(2)/2)/2=sin^2(67.5)
(sqrt(2)+1)/(2sqrt(2))=sin^2(67.5)

Answer 2

ohhhhh

thank you for typing all that out so clearly :3