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Question

In △ABC,1−tan A2 tan B2=
[Roorkee 1973]


A

2ca+b+c

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B

aa+b+c

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C

2a+b+c

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D

4aa+b+c

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Solution

The correct option is A

2ca+b+c


1tanA2 tan B2=cosA2cosB2sinA2sinB2sinB2cosA2cosB2
=cos(A2+B2)cosA2cosB2=sinC2cosA2cosB2
=[(sa)(sb)bc.acab.s(sa)s(sb)]1/2=cs=2ca+b+c.


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