Problem: If, $A+B+C=90\xb0$ then find the minimum value of $13{\mathrm{tan}}^{2}(A)+9{\mathrm{tan}}^{2}(B)+{\mathrm{tan}}^{2}(C)$ .

Carly Cannon
2022-07-05
Answered

Problem: If, $A+B+C=90\xb0$ then find the minimum value of $13{\mathrm{tan}}^{2}(A)+9{\mathrm{tan}}^{2}(B)+{\mathrm{tan}}^{2}(C)$ .

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bap1287dg

Answered 2022-07-06
Author has **13** answers

Step 1

Hint

$\sum _{\text{cyc}}(p\mathrm{tan}A-q\mathrm{tan}B{)}^{2}\ge 0$

Solve for $\frac{{p}^{2}+{u}^{2}}{13}}=\cdots =m$

$pq=rs=tu=n$ to use

$\sum _{\text{cyc}}\mathrm{tan}A\mathrm{tan}B=1$

Hint

$\sum _{\text{cyc}}(p\mathrm{tan}A-q\mathrm{tan}B{)}^{2}\ge 0$

Solve for $\frac{{p}^{2}+{u}^{2}}{13}}=\cdots =m$

$pq=rs=tu=n$ to use

$\sum _{\text{cyc}}\mathrm{tan}A\mathrm{tan}B=1$

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