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Question

If A+B=225°, then cotA1+cotAcotB1+cotB=


A

1

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B

-1

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C

0

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D

12

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Solution

The correct option is D

12


Explanation for the correct option :

Step 1 : Expressing the given data:

Given A+B=225°

Taking " cot " on both sides, cot(A+B)=cot225°

cotAcotB1cotA+cotB=1 [cot(180°+45°)=cot45°=1]

cotAcotB1=cotA+cotB

cotAcotB=1+cotA+cotB…..(i)

Step 2: Simplification of [cotA1+cotA][cotB1+cotB]

Now, cotA1+cotAcotB1+cotB=cotAcotB(1+cotB)(1+cotA)

=cotAcotB1+cotA+cotB+cotAcotB

=cotAcotBcotAcotB+cotAcotB

=cotAcotB2cotAcotB

[cotA1+cotA][cotB1+cotB]=12

Hence, option "D" is correct.


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