If A - B -225-1- A 1- B equal toA- A BB- 2 A- BC- 2 Acot BD- A- B

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). Bef ...

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Byju's Answer

Standard XI

Mathematics

Distinguish Acute Angle Bisectors and Obtuse Angle Bisectors

If A + B =225...

Question

If A+B = $225^{\circ}$ , (1+cotA)(1+cotB) equal to

cotAcotB

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2 (cotA+cotB)

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2cotAcotB

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cotA+cotB

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Solution

The correct option is C
2cotAcotB

After seeing A+B= $225^{\circ}$ 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) = $\frac{c o t A c o t B - 1}{c o t A + c o t B}$

( Cot(A +B) = cot $225^{\circ}$ = cot(180 + 45) = cot $45^{\circ}$ = 1 )

$\Rightarrow$ 1 = $\frac{c o t A c o t B - 1}{c o t A + c o t B}$

$\Rightarrow$ cotA + cotB = cotAcotB - 1
We will replace cotA + cotB with cotAcotB-1 in out expression.
$\Rightarrow 1 + c o t A c o t B + c o t A + c o t B$
$= 1 + c o t A c o t B + c o t A c o t B - 1$
$= 2 c o t A c o t B$
Key steps : (1) cot (A+B) $= x \frac{c o t A c o t B - 1}{c o t A + c o t B}$
(2) Expanding the expression and guessing that we have to use cot(A+B).

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

If A+B = $225^{\circ}$ , (1+cotA)(1+cotB) equal to