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Question

Assertion :In a ΔABC, (a+b+c)(tanA2+tanB2)=2ccotC2 Reason: In a ΔABC a=bcosC+ccosB

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 is incorrect but Reason is correct
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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Assertion:
Consider, (a+b+c)[tanA2+tanB2]
=(a+b+c)tan(A2+B2)[1tanA2tanB2]
=2stan(πC2)[1(sb)(sc)s(sa)(sa)(sc)s(sb)]
=cotC2[2s2s(sc)s]
=2ccotC2
Reason:
For any triangle ABC,
a=bcosC+ccosB
b=acosC+ccosA
c=acosB+bcosA
Hence, reason is correct but not a correct explanation of assertion.

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