By using the formula which expresses sin a and cos a in terms of t , where t= tan (a/2) , show that

(1+sin a)/(5+4 cos a )=(1+t)^2/(9+t^2)

I can do this part .

Deduce that $\displaystyle 0\leq\frac{1+\sin a}{5+4 \cos a}\leq\frac{10}{9}$ for all values of a .

I cant figure out this part .