$\lim\limits_{h\to 0}\large\frac{(a+h)^2\sin(a+h)-a^2\sin a}{h}$
$\Rightarrow \lim\limits_{h\to 0}\large\frac{a^2[\sin(a+h)-\sin a]+2ah\sin(a+h)+h^2\sin(a+h)}{h}$
$\Rightarrow \lim\limits_{h\to 0}\large\frac{a^2[2\cos(a+h/2)\sin h/2]}{2\times h/2}+$$2a\sin(a+h)+h\sin(a+h)$
$\Rightarrow a^2\cos a+2a\sin a$
Hence (a) is the correct answer.