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If x, y, z be all positive acute angles, then find the least value of tan x (cot y + cot z) + tan y (cot z + cotx) +tan z (cot x + cot y).y) |
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Answer» If a number m is positive so m+ m 1
≥2 So, we will use this rule here, tanx(coty+cotz)+tany(cotz+cotx)+tanz(cotx+coty) =tanx( tany 1
+ tanz 1
)+tany( tanz 1
+ tanx 1
)+tanz( tanx 1
+ tany 1
) = tany tanx
+ tanz tanx
+ tanz tany
+ tanx tany
+ tanx tanz
+ tany tanz
=( tany tanx
+ tanx tany
)+( tanz tanx
+ tanx tanz
)+( tanz tany
+ tany tanz
) =(a+ a 1
)+(b+ b 1
)+(c+ c 1
) where a= tany tanx
,b= tanz tany
,c= tanx tanz
≥2+2+2(from above) ≥6 So, MINIMUM value is 6 |
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