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If A +B+C= pi and m/C is obtuse then t...

If `A +B+C= pi and m/_C` is obtuse then `tan A. tan B` is

A

`tanAtanBgt1`

B

`tanAtanBlt1`

C

tanAtanB=1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`A+B+C=pi`
`A+B=pi-C`
`impliestan(A+B)=tan(pi-C)`
`implies(tanA+tanB)/(1-tanAtanC)=tan(pi-C)`
`implies (tanA+tanB)/(1-tanAtanC)=-tanC`
Now, C is an obtuse angle, hence
`implies tanClt0`
`implies -tanCgt0`
`implies (tanA+tanB)/(1-tanAtanB)gt0`
`implies 1-tanAtanBgt0` [`because` A, B are acute angles, `therefore tanAgt0, tanBgt0`]
`=tanAtanBlt1`
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