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Assertion :(A): If A>0 & B>0,A+B=π6, then the maximum value of tanAtanB is 742 Reason: (R): If x1+x2+x3+.......xn=λ(constant), then value of x1,x2,x3,.......xn is greatest when x1=x2=x3=.......xn

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
Both Assertion flase 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 Assertion
Assertion:
A+B=π6
tan(A+B)=tanπ6
tanA+tanB1tanAtanB=13
1tanAtanB=3(tanA+tanB)
tanAtanB=13(tanA+tanB)
So, tanAtanB is maximum when tanA+tanB is minimum.
And this is only possible when tanA=tanB=π12
Hence,
max(tanAtanB)=tan2π12=(23)2=743
Reason is true
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

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