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In triangle A B C , if /A=pi/4, then fin...

In triangle `A B C ,` if `/_A=pi/4,` then find all possible values of `tanBtanCdot`

Text Solution

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`A+B+C=pi`
`angle A=(pi)/(4)rArr B+C=(3pi)/(4)`
Let `tan B tan C=x`
`rArr tan B tan ((3pi)/(4)-B)=x`
`rArr tanB(tan""(3pi)/(4)-tan B)/(1+tan""(3pi)/(4)tan B)=x`
`rArr(-tan B-tan^(2)B)/(1-tanB)=x`
`rArr tan^(2)B+(1-x)tan B+x=0`
Now, `tan B` is real.
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