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Question

Assertion :If tanA+tanB+tanC=3√3, then triangle is equilateral Reason: In ΔABC,tanA+tanB+tanC=tanAtanBtanC.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion false but Reason is true
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionIn a triangle A+B+C=πA+B=π−Ctan(A+B)=tan(π−C)tanA+tanB1−tanAtanB=−tanCtanA+tanB=−tanC+tanAtanBtanCtanA+tanB+tanC=tanA.tanB.tanCFor an equilateral triangle.A=B=C=600HencetanA.tanB.tanC=(√3)3=3√3=tanA+tanB+tanC

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