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Q.

In triangle ABC , tanA+ tan B + tanC= 6 and tanA tanB = 2.then the values of tanA, tanB, tanc are, respectively

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a

1, 2, 3

b

3, 2/3, 7/3

c

none of these

d

4, 1/2, 3/2

answer is A.

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Detailed Solution

ln a triangle, tanA + tanB + tan C = tanA tanB tanC ------------(i)

6 = 2tanC 

or   tanC = 3

Also tanA + tanB = 6-3 = 3-------(ii)

By Eqs. (i) and (ii), tanA and tanB are roots of  x2 -3x + 2 = 0. 

Thus,
tanA, tan B = 2, 1 or 1,2 and tanC = 3

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