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If then the maximum value of tan A tan B is
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By Expert Faculty of Sri Chaitanya
a
13
b
13
c
3
d
3
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Correct option is B
Given A+B=60∘ or B=60∘−A∴ tan B=tan60∘−A=3−tan A1+3tan A Now z=tan Atan Bor z=t(3−t)1+3t=3t−t21+3twhere t = tan A dzdt=−(t+3)(3t−1)(1+3t)2=0or t=1/3or t=tan A=tan 30∘The other value is rejected as both A and B are +ve acute angles.If t<13,dzdtis positive and if t>13,dzdtis negative.Hence, maximum when t=13and maximum value =13.
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