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Question

If A + B = 225, then cotA1+cotA. cotB1+cotB =

[MNR 1974]


A

1

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B

-1

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C

0

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D

1/2

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Solution

The correct option is D

1/2


cotA1+cotA. cotB1+cotB = 1(1+tanA)(1+tanB)

= 1tanA+tanB+1+tanAtanB

[ ∵ tan(A + B) = tan225]

tanA + tan B = 1 - tan A tan B

= 11tanAtanB+1+tanAtanB = 12.


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