Range for projection angle " \(\alpha\) "

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

Range for projection angle " \(\beta\) "

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

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

\(\Rightarrow \beta=90^{\circ}-\alpha\)

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

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

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

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