If a-cos-isin- b-cos-isin-c-cos-isin- and b-c-c-a-a-b-1-Thencos-cos-cos- is equal to

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 XIII

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

\frac{3}{2}

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\frac{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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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 1bc=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