In a ` A B C ,` if `tanA:tanB :tanC=3:4:5,` then the value of `sinA sinB sinC` is equal to (a)`2/(sqrt(5))` (b) `(2sqrt(5))/7` `(2sqrt(5))/9` (d) `2/(3sqrt(5))`

Explanation

Let `tanA = 3k, tanB = 4k, tanC = 5k`

As, `A+B+C = pi`

`:. tanA+tanB+tanC = tanAtanBtanC`

`=>3k+4k+5k = 3k*4k*5k`

`=>12k = 60k^3`

`=>k^2 = 1/5`

`=> k = 1/sqrt5`

`:. tan A = 3/sqrt5, tanB = 4/sqrt5, tanC = 5/sqrt5 = sqrt5`

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