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In triangleABC, if tanA : tanB : tanC = ...

In `triangleABC`, if `tanA : tanB : tanC = 1:2:3`, then `sinA:sinB:sinC` =?

Text Solution

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Let `tan A = k`
Then, `tanB = 2k and tanC = 3k`
We know, `A+B+C = pi`.So, `C = pi-(A+B)`
`tanC = 3k => tan(pi-(A+B)) = 3k`
`=>tan(A+B) = -3k`
`=>(tanA+tanB)/(1-tanAtanB) = -3k`
`=>(k+2k)/(1-k(2k)) = -3k`
`=>3k = -3k(1-2k^2)`
...
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