If a sin- b sin-2 -3- c sin-4 -3- then the value of ab - bc - ca -

Let asinθ=bsin(θ+2π3)=csin(θ+4π3)=λ ⇒λ a=sinθ, λ b=sin(θ+2π3) and λ c=sin(θ+4π3) ⇒λ a+λ b+λ c=sinθ+sin(θ+2π3)+sin(θ+4π3) =2sin(θ+2π3)cos(2π3)+sin(θ+2π3) = sin(θ ...

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

Byju's Answer

Standard XII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

If a sinθ= b ...

Question

If $a sin θ = b sin (θ + \frac{2 π}{3}) = c sin (θ + \frac{4 π}{3})$ , then the value of $a b + b c + c a =$

Open in App

Solution

Let $a sin θ = b sin (θ + \frac{2 π}{3}) = c sin (θ + \frac{4 π}{3}) = λ$
$\Rightarrow \frac{λ}{a} = sin θ, \frac{λ}{b} = sin (θ + \frac{2 π}{3})$
and $\frac{λ}{c} = sin (θ + \frac{4 π}{3})$
$\Rightarrow \frac{λ}{a} + \frac{λ}{b} + \frac{λ}{c} = sin θ + sin (θ + \frac{2 π}{3}) + sin (θ + \frac{4 π}{3})$
$= 2 sin (θ + \frac{2 π}{3}) cos (\frac{2 π}{3}) + sin (θ + \frac{2 π}{3})$
$= - sin (θ + \frac{2 π}{3}) + sin (θ + \frac{2 π}{3})$
$\Rightarrow \frac{λ}{a} + \frac{λ}{b} + \frac{λ}{c} = 0$
$\Rightarrow λ (\frac{b c + c a + a b}{a b c}) = 0$
$\Rightarrow a b + b c + a c = 0$

Suggest Corrections

Similar questions

If $2 t a n \frac{α}{2} = t a n \frac{β}{2},$ prove that $c o s α = \frac{3 + 5 c o s β}{5 + 3 c o s β} .$ A.so, determine the value of $c o s α$ when $β = 60^{\circ} .$