According to the Cauchy's inequality (lm+mn+nl)2≤(l2+m2+n2)2
⇒‌‌(lm+mn+nl)2≤1‌‌{∵l2+m2+n2=0}
⇒‌‌−1≤(Im+mn+nl)≤1 Therefore, the maximum value of lm+mn+nl=1 and it is possible only when l=m=n, as l=cos‌α, m=cos‌β and n=cos‌γ, so α=β=γ