Question

Prove the identity84x%29%20%7D%7B%20%5Ccos%282x%29%20%7D%20" id="TexFormula1" title="4 \sin(x) \cos(x) = \frac{ \sin(4x) }{ \cos(2x) } " alt="4 \sin(x) \cos(x) = \frac{ \sin(4x) }{ \cos(2x) } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

Below

Step-by-step explanation:

● 4 sin(x) cos(x) = sin(4x)/cos(2x)

Let's prove that:

● 4 sin(x) cos(x) cos(2x) = sin(4x)

It's easier to prove it than the first one

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● 4 sin(x) cos(x) cos (2x)

● [2 sin(x) cos(x)] 2 cos(2x)

We khow that [2 sin(x) cos(x)]= sin(2x)

So:

● sin(2x) 2 cos(2x)

Based on the same relation

● sin(4x)

It's proved

Answer 2

=> R.H.S

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

$= \frac{ 2 \sin(2x) \cos(2x) }{ \cos(2x) }$

$= 2 \sin(2x)$

$= 2(2 \sin(x) \cos(x) )$

$= 4 \sin(x) \cos(x)$

R.H.S = L.H.S

PROVED!