If a-cos-isin- b-cos-isin-c - cosy - isin - and b-c-c-a-a-b-1- Thencos -cos -cos - is equal toA- 3 - 2B- -3 - 2C- 0D- 1

B/c=cosβ + isinβ/cosγ + isinγ×cosγ isinγ/cosγ isinγ ⇒b/c= cos(β γ)+isin(β γ) .....(i) Similarly, c/a = cos(γ α)+isin(γ α) .......(ii) And a/b = cos(α β)+ ...

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Byju's Answer

Standard XII

Mathematics

Polar Representation of a Complex Number

If a=cosα+isi...

Question

If a=cos $α$ +isin $α$ , b=cos $β$ +isin $β$ ,

c=cos $γ$ +isin $γ$ and $\frac{b}{c}$ + $\frac{c}{a}$ + $\frac{a}{b}$ =1,Then

cos( $β$ - $γ$ )+cos( $γ$ - $α$ )+cos( $α$ - $β$ ) is equal to

3/2

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-3/2

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Solution

The correct option is D
1

$\frac{b}{c}$ = $\frac{c o s β + i s i n β}{c o s γ + i s i n γ} \times \frac{c o s γ - i s i n γ}{c o s γ - i s i n γ}$

$\Rightarrow \frac{b}{c} = c o s (β - γ) + i s i n (β - γ) . . . . . (i)$

Similarly, $\frac{c}{a} = c o s (γ - α) + i s i n (γ - α) . . . . . . . (i i)$

And $\frac{a}{b} = c o s (α - β) + i s i n (α - β) . . . . . . . (i i)$

Equating real and imaginary parts,

$c o s (β - γ) + c o s (γ - α) + c o s (α - β) = 1$

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Similar questions

If a=cos $α$ +isin $α$ , b=cos $β$ +isin $β$ ,

c=cos $γ$ +isin $γ$ and $\frac{b}{c}$ + $\frac{c}{a}$ + $\frac{a}{b}$ =1,Then

cos( $β$ - $γ$ )+cos( $γ$ - $α$ )+cos( $α$ - $β$ ) is equal to

Q. If

a = cos α + i sin α, b = cos β + i sin β,

c = cos γ + i sin γ

and

\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = 1,

then

Q. If

a = cos α + i sin α, b = cos β + i sin β, c = cos γ + i sin γ

and

\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = - 1

, then

cos (β - γ) + cos (γ - α) + cos (α - β) =

Q. If

α = c o s α + i s i n α, b = c o s β + i s i n β, c = c o s γ + i s i n γ

and

\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 1

then

c o s (β - γ) + c o s (γ - α) + c o s (α - β) i s e q u a l t o

Prove that,

(i) $c o s α + c o s β + c o s γ + c o s (α + β + γ) = 4 c o s (\frac{α + β}{2}) . c o s (\frac{β + γ}{2}) . c o s (\frac{γ + α}{2}) .$

(ii) If $t a n x = \frac{b}{a},$ then $\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}} = \frac{2 c o s x}{\sqrt{c o s 2 x}} .$

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If a=cosα+isinα, b=cosβ+isinβ, c=cosγ+isinγ and bc+ca+ab=1,Then cos(β-γ)+cos(γ-α)+cos(α-β) is equal to

The correct option is D 1 bc=cosβ+isinβcosγ+isinγ×cosγ−isinγcosγ−isinγ ⇒bc=cos(β−γ)+isin(β−γ).....(i) Similarly, ca=cos(γ−α)+isin(γ−α).......(ii) And ab=cos(α−β)+isin(α−β).......(ii) Equating real and imaginary parts, cos(β−γ)+cos(γ−α)+cos(α−β)=1

If a=cos $α$ +isin $α$ , b=cos $β$ +isin $β$ ,

c=cos $γ$ +isin $γ$ and $\frac{b}{c}$ + $\frac{c}{a}$ + $\frac{a}{b}$ =1,Then

cos( $β$ - $γ$ )+cos( $γ$ - $α$ )+cos( $α$ - $β$ ) is equal to