Question

prove that .. 4 sin A× sin ( 60° + A)× sin (60°- A)= sin 3 A

Answer 1

$\bold{Hay Mate Its ur Answer}$

LHS=>

4 sinA ×sin(60°+A)×sin(60°-A)

4 Sin A(Sin²60°-Sin²A)

$\bold{we know that sin60= root 3/2 }$

$4 \: sin \: a(( \frac{ \sqrt{3} }{2} ) {}^{2} - {sin}^{2} a)$

$\italic{If we know that (root 3/2)^2=root 3/4}$

$4 \: sin \: a( \frac{3}{4} - sin {}^{2} a)$

$4(3 \: sin \: a - 4 \: {sin}^{3} \frac{a}{4} )$

$\bold{Let the 4 common}$

$4 \times \frac{1}{4} (sin3a)$

sin3A

$\box{Sin3A}$

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