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Question

If A+B =225, (1+cotA)(1+cotB) equal to


A

cotAcotB

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B

2 (cotA+cotB)

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C

2cotAcotB

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D

cotA+cotB

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Solution

The correct option is C

2cotAcotB


After seeing A+B=225 and cotA and cotB in the expression to be evaluated, it becomes an obvious guess to use cot (A+B).

Before using that, let us try to expand our expansion.
(l+cotA) (l+cotB) = 1+cotAcotB+cotA+cotB
After seeing cotAcotB and cotA+cotB., it becomes more evident that we have to use cot (A + B)
cot (A+B) = cotAcotB1cotA+cotB

( Cot(A +B) = cot225= cot(180 + 45) = cot45 = 1 )

1 = cotAcotB1cotA+cotB

cotA + cotB = cotAcotB - 1
We will replace cotA + cotB with cotAcotB-1 in out expression.
1+cotAcotB+cotA+cotB
=1+cotAcotB+cotAcotB1
=2cotAcotB
Key steps : (1) cot (A+B) =xcotAcotB1cotA+cotB
(2) Expanding the expression and guessing that we have to use cot(A+B).


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