①(sin67.5)^4-(cos67.5)^4
=[(sin67.5)^2+(cos67.5)^2][(sin67.5)^2-(cos67.5)^2]
=-cos135=cos45=√2/2
②sin2a=2tana/[1+(tana)^2]=-4/5
cos2a=[1-(tana)^2]/[1+(tana)^2]
=(1-4)/(1+4)=-3/5
∴sin4a=2sin2acos2a=2(-4/5)(-3/5)=24/25
①(sin67.5)^4-(cos67.5)^4
=[(sin67.5)^2+(cos67.5)^2][(sin67.5)^2-(cos67.5)^2]
=-cos135=cos45=√2/2
②sin2a=2tana/[1+(tana)^2]=-4/5
cos2a=[1-(tana)^2]/[1+(tana)^2]
=(1-4)/(1+4)=-3/5
∴sin4a=2sin2acos2a=2(-4/5)(-3/5)=24/25