Question

Assertion :If $A,B,C$ are the angles of a triangle such that angle $A$ is obtuse then $\tan B\tan C>1$. Reason: In any triangle ABC $\tan A=\frac{\tan B+\tan C}{\tan B\tan C-1}$.

• 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 D Assertion is incorrect but Reason is correct

Reason is true as

In $△ABCA+B+C=\pi$

$\tan A=\tan \left(\pi \right(B+C\left)\right)=-\tan (B+C)$

$\Rightarrow \tan A=\frac{\tan B+\tan C}{\tan B\tan C-1}.....\left(1\right)$

Assertion

If A is obtuse and $B,C$ are acute

$\Rightarrow \tan A<0$ and $\tan B,\tan C>0$

So from $\left(1\right)$ we get

$\tan B\tan C<1$

hence assertion is false.