From the figure,
cot β = \(\frac{BD}{H_{max}}\)
and cot γ =\(\frac{DC}{H_{max}}\)
cot β + cot γ =\(\frac{DC+DC}{H_{max}}\)
\(\frac{Range}{H_{max}}\)
⇒ cot β + cot γ = \(\frac{(u^2sin\,2α)/g}{(u^2sin^2α)/2g}\)
⇒ cot β + cot γ = 2 × \(\frac{2sin\,α\,cos\,α}{sin^2α }\)
cot β + cot γ = 4 cot α.