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Question

If A,B,C are angles of a triangle and angle A is obtuse, then the exhaustive set of value of tanBtanC is

A
(0,1)
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B
(0,2)
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C
(0,0.5)
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D
any positive real number
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Solution

The correct option is A (0,1)
A+B+C=πB+C=πAtanA=tan(B+C)tanA=tanB+tanCtanBtanC1
As angle A is obtuse angle and rest other angles are acute, so
tanA<0,tanB>0,tanC>0tanB+tanCtanBtanC1<0
tanBtanC<1
Therefore, tanBtanC(0,1)

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