Question

#QualityQuestion
@Trigonometry

$\rm{Prove~ the~ identity~ :}$
4 sin(x) cos(x) = sin(4x) / cos(2x)​

Answer 1

~Solution :-

• We can prove the identity as follows;

$\large \mathcal{LHS :}$

$\sf{ \frac{sin(4x) }{ cos(2x)}}$

$\to \sf{ \frac{ 2 sin(2x) cos(2x) }{ cos(2x)}}$

$\to \sf{ \sf{ \frac{ 2 sin(2x) \cancel{cos(2x) }}{ \cancel{ cos(2x)}}} }$

$\to \sf{ 2 sin(2x)}$

$\to \sf{ 2 [ 2 sin(x) cos(x)]}$

$\implies \bf \red{ 4 sin(x) cos(x) }$

$\large \mathcal{ : RHS}$

• Hence, Proved!!!

— BrainlyROME —

Answer 2

Answer:

Step-by-step explanation: