Question

Assertion :If triangle ABC is equilateral then $tanA+tanB+tanC=3\sqrt{3}$ Reason: In $\Delta ABC$,$\tan A+\tan B+\tan C=\tan A\tan B\tan C$

• 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 false but Reason is true

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion:is true as
In equilateral $△ABC$ $\angle A=\angle B=\angle C=\frac{\pi }{3}$

$tanA+tanB+tanC=3tan\frac{\pi }{3}=3\sqrt{3}$

Reason is true as
$A+B+C=\pi \Rightarrow A+B=\pi -C$

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

$\Rightarrow \frac{\tan A+\tan B}{1-\tan A\tan B}=-\tan C$

$\Rightarrow \tan A+\tan B+\tan C=\tan A\tan B\tan C$

But the reason is not the correct explanation of the assertion