Question

Assertion :In any $\Delta$ABC, if A is obtuse, then tan B tan C < 1 Reason: If any triangle ABC cot A + cot B + cot C $=$ cot A cot B cot C

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

If A is obtuse then $B$ and $C$ are acute.
Therefore $tanB$ and$tanC$ are positive.
However
$tanA=\frac{tanB+tanC}{1-tanA.tanB}$ is negative.
Then $1-tanAtanB$ has to be negative.
$1-tanA.tanB<0$
$tanA.tanB<1$.