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Statement-1: If A, B, C are the angles o...

Statement-1: If A, B, C are the angles of a triangle such that angle A is obtuse, then tan `C gt1.`
Statement-2: In any `DeltaABClt` we have `tanA=(tanB+tanC)/(tanBtanC-1)`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement -1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
D
In any `DeltaABC,` we have
`A+B+C=pi`
`impliesA=pi-(B+C)`
`impliestanA=-tan(B+C)`
`impliestanA=(tanB+tanC)/(tanBtanC-1)`
So, statement-2 is true.
If angle A is obtuse, then B and C are actue angles.
`thereforetanAlt0, tanBgt0and tanCgt0`
`implies(tanB+tanC)/(tanBtanC-1)lt0impliestanBtanClt1`
So, statement-2 is true.
If angle A is obtuse, then B and C are acute angles.
`thereforetanA lt0, tanBgt0and tanCgt0`
`implies(tanB+tanC)/(tanBtanC-1)lt0impliestanBtanClt1`
So, statement-1 is not correct.
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