If sin 3 α=4 sin α sin (x+α) sin (x-α), then x=

Question

If sin 3 α=4 sin α sin (x+α) sin (x-α), then x= (A) n π ± (π/6) (B) n π ± (π/3) (C) n π ± (π/4) (D) n π ± (π/2)

Tardigrade Admin · Accepted Answer

sin 3 α=4 sin α sin (x+α) sin (x-α) ∴ sin 3 α=4 sin α( sin 2 x cos 2 α- cos 2 x sin 2 α) ∴ 3 sin α-4 sin 3 α=4 sin α( sin 2 x- sin 2 α) ∴ sin 2 x=((3/4)) ⇒ sin 2 x= sin 2 (π/3) ∴ x= n π ± (π/3)

Q. If $sin 3 α = 4 sin α sin (x + α) sin (x - α)$ , then $x =$

$nπ \pm \frac{π}{6}$

$nπ \pm \frac{π}{3}$

$nπ \pm \frac{π}{4}$

$nπ \pm \frac{π}{2}$

$sin 3 α = 4 sin α sin (x + α) sin (x - α)$
$∴ sin 3 α = 4 sin α (sin^{2} x cos^{2} α - cos^{2} x sin^{2} α)$
$∴ 3 sin α - 4 sin^{3} α = 4 sin α (sin^{2} x - sin^{2} α)$
$∴ sin^{2} x = (\frac{3}{4}) \Rightarrow sin^{2} x = sin^{2} \frac{π}{3} ∴ x = nπ \pm \frac{π}{3}$

Q. If sin3α=4sinαsin(x+α)sin(x−α), then x=

nπ±6π​

nπ±3π​

nπ±4π​

nπ±2π​