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Question

# Assertion :If triangle ABC is equilateral then tanA+tanB+tanC=3√3 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for AssertionAssertion:is true asIn equilateral △ABC ∠A=∠B=∠C=π3tanA+tanB+tanC=3tanπ3=3√3Reason is true as A+B+C=π⇒A+B=π−Ctan(A+B)=tan(π−C)=−tanC⇒tanA+tanB1−tanAtanB=−tanC⇒tanA+tanB+tanC=tanAtanBtanCBut the reason is not the correct explanation of the assertion

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