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If tan^2(pi-A)/4+tan^2(pi-B)/4+tan^2(pi-...

If `tan^2(pi-A)/4+tan^2(pi-B)/4+tan^2(pi-C)/4=1` , then ` A B C` is equilateral (b) isosceles (c) scalene (d) none of these

A

equilateral

B

isosceles

C

scalene

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
Let `alpha=(pi-A)/(4),beta(pi-B)/(4),gamma=(pi-C)/(4)`
`rArr alpha+beta+gamma=(pi)/(2)`
`sum tan alpha tan beta=1`
`rArr sum tan^(2)alpha=1sum tan alpha tan beta`
`rArr tan alpha=tan beta=tan gamma`
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