Statement-1: In any `DeltaABC` if A is obtuse, then tanBtanC`lt1`
Statement-2: In any `!ABC`, we have
tan A + tan B + tan C = tan A tan B tan C

Options

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.

Explanation

In any `DeltaABC`, we have
`A+B+C=pi`
`rArrtan (A + B + C) = tan pi`
`rArr(tanA+tanB+tanC-tanAtanBtanC)/(1-tanAtanB-tanBtanC-tanCtanA)=0`
`rArrtan A + tan B + tan C = tan A tan B tan C`
So, statement- 2 is true.
Now,
tan A + tan B + tan C = tan A tan B tan C
`rArrtanA=-(tanB+tanC)/(1-tanBtanC)`
`rArr(tanB+tanC)/(1-tanBtanC)gt0[because`A is obtuse `thereforetanAlt0]`
`rArrtanBtanClt1`
So, statement-1 is true and statement-2 is a correct explanation for statement- 1.