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Question

If A,B,C are the angles of a triangle such that the angle A is obtuse, then tanBtanC<

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is B 1
A is obtuse angle.
Then π2<A<π
π2<π(B+C)<π
π2>π+(B+C)>π
π2>(B+C)>0
B+C<π2
B<π2C
tanB<tan(π2C)
tanB<cotC
tanB<1tanC
Hence tanBtanC<1

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