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Likurg_2 [28]
3 years ago
8

Prove the identity

84x%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">
​

Mathematics
2 answers:
kolbaska11 [484]3 years ago
6 0

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

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 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

alukav5142 [94]3 years ago
5 0

=> 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

<u>P</u><u>R</u><u>O</u><u>V</u><u>E</u><u>D</u><u>!</u>

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