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If 3tanα+4tanβ+5tanγ=λ,then the minimum value of tan²α+tan²β+tan²γ is a.λ²/9 b.λ²/16 c.λ²/25 d.none of these

If 3tanα+4tanβ+5tanγ=λ,then the minimum value of tan²α+tan²β+tan²γ is


a.λ²/9


b.λ²/16


c.λ²/25


d.none of these

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Menka,

 

Consider vectors:

A = 3i+4j+5k,

B = tanxi + tanyj + tanzk

 

A(dot)B = 3tanx+4tany+5tanz = λ.

Now A(dot)B ≤ |A| |B|.

So minimum value of the given expression would be λ2/50.

 

Hence (D).

 

Hope that helps.

Best Regards,

Ashwin (IIT Madras).

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