$\text { Range }=\frac{ u ^2 \sin 2 \theta}{ g }$

Range for projection angle " $\alpha$ "

$R _1=\frac{ u ^2 \sin 2 \alpha}{ g }$

Range for projection angle " $\beta$ "

$R _2=\frac{ u ^2 \sin 2 \beta}{ g }$

$\alpha+\beta=90^{\circ}(\text { Given })$

$\Rightarrow \beta=90^{\circ}-\alpha$

$R _2=\frac{ u ^2 \sin 2\left(90^{\circ}-\alpha\right)}{ g }$

$R _2=\frac{ u ^2 \sin \left(180^{\circ}-2 \alpha\right)}{ g }$

$R _2=\frac{ u ^2 \sin 2 \alpha}{ g }$

$\Rightarrow \frac{ R _1}{ R _2}=\frac{\left(\frac{ u ^2 \sin 2 \alpha}{ g }\right)}{\left(\frac{ u ^2 \sin 2 \alpha}{ g }\right)}=\frac{1}{1}$