Question

4 sin x sin (pi/3 -x) sin (pi/3+x) = sin 3x ...Prove​

Answer 1

Answer:

$\bf{4\:sinx\:sin(\pi/3-x)\:sin(\pi/3+x)=sin3x}$

Step-by-step explanation:

4 sin x sin (pi/3 -x) sin (pi/3+x) = sin 3x

Formula used:

$cos(A-B)-cos(A+B)=2\:sinA\:sinB$

$cos2A=1-2sin^2A$

$4\:sinx\:sin(\pi/3-x)\:sin(\pi/3+x)$

$=2\:sinx\:[2sin(\pi/3-x)\:sin(\pi/3+x)]$

$=2\:sinx\:[cos((\pi/3-x)-(\pi/3+x))-cos((\pi/3-x)+(\pi/3+x))]$

$=2\:sinx\:[cos(-2x)-cos(2\pi/3)]$

$=2\:sinx\:[cos2x-(\frac{-1}{2})]$

$=2\:sinx\:[cos2x+\frac{1}{2}]$

$=2\:sinx\:[1-2sin^2x+\frac{1}{2}]$

$=2\:sinx\:[\frac{3}{2}-2sin^2x]$

$=2\:sinx(\frac{3}{2})-2sinx(2sin^2x)]$

$=3\:sinx-4sin^3x$

$=sin3x$

Answer 2

Answer:plz notice the attachment file

Step-by-step explanation: