If range is same then, one angle is \(\theta\) and other angle is \((90-\theta)\)

\(\Rightarrow h_1=\frac{u^2 \sin ^2 \theta}{2 g}, h_2=\frac{u^2 \sin ^2(90-\theta)}{2 g}\)

\(h_1=\frac{u^2 \sin ^2 \theta}{2 g}, h_2=\frac{u^2 \cos ^2 \theta}{2 g}\)

So, \(h_1+h_2 \Rightarrow \frac{u^2 \sin ^2 \theta}{2 g}+\frac{u^2 \cos ^2 \theta}{2 g}=\frac{u^2}{2 g}\left(\sin ^2 \theta+\cos ^2 \theta\right)\)

\(h_1+h_2=\frac{u^2}{2 g}\)