Question

Assertion :If A is obtuse angle in $\Delta ABC,$ then $\tan B\tan C<1$ Reason: In $\Delta ABC,\tan A=\frac{\tan B+\tan C}{\tan B\tan C-1}$

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

If A is obtuse than $0<B+C<{90}^{\circ }\Rightarrow \tan (B+C)=\frac{\tan B+\tan C}{1-\tan B\tan C}>0$
as numerator is positive
$1-\tan B\tan C>0\tan B\tan C<1$
Reason is obviously true & explain assertion