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If A+B+C=pi/2, then find the value of ta...

If `A+B+C=pi/2`, then find the value of `tanAtanB+tanBtanC+tanCtanA`

A

0

B

1

C

`-1`

D

tan A tan B tan C

Text Solution

Verified by Experts

The correct Answer is:
B
Given `A+B+C=(pi)/(2)`
Take tan on both sides ,
`rArrtan(A+B)+tan((pi)/(2))`
`rArr(tanA+tanB+C-tanAtanBtanC)/(1-tanAtanB-tanBtanC-tanCtanA)=(1)/(0)(because(1)/(0)=oo)`
`rArrtanAtanB+tanBtanC+tanCtanA=1`
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