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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 (cotA+cotB)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2cotAcotB

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

cotA+cotB

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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).

Suggest Corrections

Similar questions

Q. If

{tan}^{- 1} (\frac{a}{x}) + {tan}^{- 1} (\frac{b}{x}) = \frac{π}{2},

then

x

is equal to

If a+b = 225, then cot a/(1 + cot a )*cot b/(1+cot b) =

If sin α + sin β = a

and

cos α + cos β = b

, then the value of

sin (α + β)

is equal to

Q. If

A_{1}, A_{2}

be two arithmetic means and

G_{1}, G_{2}

be two geometric means between two positive numbers

a

and

b,

then

(\frac{A_{1} + A_{2}}{G_{1} G_{2}})

is equal to

Q. Vectors

\vec{a} and \vec{b}

are inclined at angle θ = 120°. If

|\vec{a}| = 1, |\vec{b}| = 2,

then

{[(\vec{a} + 3 \vec{b}) \times (3 \vec{a} - \vec{b})]}^{2}

is equal to
(a) 300
(b) 325
(c) 275
(d) 225

Join BYJU'S Learning Program

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

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