Q.
The least value of secA+secB+secC in a acute angled triangle
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a
−18
b
332
c
−12
d
6
answer is D.
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Detailed Solution
In ΔABC ,A,B,C are acute. ⇒secA,secB,secC are positive Now, A·M≥H·M.secA+secB+secC3≥3cosA+cosB+cosC →1We have cosA+cosB+cosC3≤cosA+B+C3 ≤cos60°∴ cosA+cosB+cosC≤32 →2From (1) and (2) secA+secB+secC≥6
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