If the points acos- -isin- - bcos-isin- and ccos- -isin- are collinear- then find -z- where- z - bcsin- - - - casin-absin- - 3i

Since, a(cos nbsp;α +isin nbsp;α ) , b(cos nbsp;β +isin nbsp;β ) amp; c(cos nbsp;γ +isin nbsp;γ ) are collinearTherefore, | ...

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Distance Formula

If the points...

Question

If the points $a (cos α + i sin α), b (cos β + i sin β)$ and $c (cos γ + i sin γ)$ are collinear, then find $| z |$ where:
$z = b c sin (β - γ) + c a sin (γ - α) + a b sin (α - β) + 3 i$

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a (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)

| z |

z = b c s i n (β - γ) + c a s i n (γ - α) + a b s i n (α - β) + 3 i - 4 k

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

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

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

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

a sin α + b sin β + c sin γ = 0

= a cos α + b cos β + c cos γ

a, b, c, \in R

- π < α, β, γ \leq π .

A = e^{i α}, B = e^{i β}, C = e^{i γ}

\sqrt{- 1} = i

∴ a A + b B + c C = 0

\frac{a}{A} + \frac{b}{B} + \frac{c}{C} = 0

(a A)^{3} + (b B)^{3} + (c C)^{3} = 3 a b c A B C

{(\frac{a}{A})}^{3} + {(\frac{b}{B})}^{3} + {(\frac{c}{C})}^{3} = \frac{3 a b c}{A B C}

sin α + 2 sin β + 3 sin γ = 0,

α + β - γ

a sin (θ + α) = b sin (θ + β)

cot θ = \frac{a cos α - b cos β}{b sin β - a sin α}

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