sin(a+h)=sinacosh+cosasinh, so (a+h)^2=a^2+2ah+h^2 and (a+h)^2sin(a+h)-a^2sina=a^2sina(cosh-1)+a^2cosasinh+2ahsinacosh+2ahcosasinh+h^2(sinacosh+cosasinh). As h tends to zero, the first term tends to zero because cosh tends to 1. sinh tends to h when h is small. The second term tends to a^2hcosa and the fourth term, 2ahcosasinh becomes 2ah^2cosa, which tends to zero as h tends to zero. The third term tends to 2ahsina. The h^2 term can be ignored because it is a second degree expression which disappears as h tends to 0. So after dividing through by h, we're left with a^2cosa+2asina, so this is the limit as h approaches zero.