cosa+sina=[1-(tana/2)^2]/[1+(tana/2)^2]+2*(tana/2)/[1+(tana/2)^2]=[1-(1/4)^2]/[1+(1/4)^2]+2*(1/4)/[1+(1/4)^2]=(15/16)/(17/16)+(1/2)/(17/16)=15/17+8/17=23/17