# Problem: If, A + B + C = 90 <mrow class="MJX-TeXAtom-ORD"> &#xB0;

Problem: If, $A+B+C=90°$ then find the minimum value of $13{\mathrm{tan}}^{2}\left(A\right)+9{\mathrm{tan}}^{2}\left(B\right)+{\mathrm{tan}}^{2}\left(C\right)$ .
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Step 1
Hint
$\sum _{\text{cyc}}\left(p\mathrm{tan}A-q\mathrm{tan}B{\right)}^{2}\ge 0$
Solve for $\frac{{p}^{2}+{u}^{2}}{13}=\cdots =m$
$pq=rs=tu=n$ to use
$\sum _{\text{cyc}}\mathrm{tan}A\mathrm{tan}B=1$