1/2sin^2a+1/3cos^2a=1/2[(1-cos2a)/2]+1/3[(1+cos2a)/2]=(1-cos2a)/4+(1+cos2a)/6=1/4+1/6-[(cos2a)/4 - (cos2a)/6]=5/12-(cos2a)/12=5/12-[1-(tana)^2 /1+(tana)^2]/12=5/12-35/444=25/74