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piyush narang Grade: 12
        

min value of


secA + secB + secC is............


 

6 years ago

Answers : (1)

Askiitians_Expert Yagyadutt
askIITians Faculty
74 Points
										

Hii Piyush


 


Look  in case of triangle...


 


cosA + cosB + cosC >= 3/2    ( as A + B + C = 180 )


 


Now apply AM>GM   =>   (cosA + cosB + cosC)/3  >=  ( cosA.cosB.cosC)^1/3


 


1/2 >= (cosA.cosB.cosC)^1/3     =>   secA.secB.secC >= 8


 


Now Again apply AM>GM


 


(secA + secB + secC)/3 >= (secA.secB.secC)^1/3


 


so for minimum value of  secA + secB + secC  ..put secA.secB.secC = minimum i.e = 8


 


So...secA + secB + secC =  3 X (8)^1/3 = 6  ans


 


 


I hope you get it


 


Regards


Yagya


askiitians_expert

6 years ago
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