d
(d) ${y_2} = \frac{A}{2}\sin \omega \,t + \frac{A}{2}\cos \omega \,t$
${y_2} = \frac{A}{2}(\sin \omega \,t + \cos \omega \,t) = \frac{A}{2} \times \sqrt 2 \;[\sin (\omega \,t + {45^o})]$
${y_2} = \frac{A}{{\sqrt 2 }}\sin (\omega \,t + {45^o})$$ \Rightarrow \frac{{{A_1}}}{{{A_2}}} = \frac{A}{{A/\sqrt 2 }} = \sqrt 2 $