Trigonometric Identity: sin(2x) = 2sin(x)cos(x)

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In this video I show a very easy to understand proof of the common trigonometric identity, sin(2x) = 2 sin(x)cos(x).

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  1. Math Easy Solutions
  2. trig
  3. trigonometry
  4. trigonometric
  5. identity
  6. identities
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Комментарии
Автор

I don't always prove trigonometric identities but when I do I sometimes just need 1 minute to do so ;)

mes
Автор

yeah you could do that too. Remember that cos(x) and sin(x) are simply ratios and thus are numbers. For example 2*4*3 = 2*3*4. This is no different than 2*cos(x)*sin(x) = 2*sin(x)*cos(x).

mes
Автор

Can you explain why you think it should be 2sin(x)*2cos(x)? The number 2 inside the sine and the number 2 outside the sine mean two completely different things. In the description I prove the identity which I used to prove sin(2x)=2sin(x)cos(x)

mes
Автор

sin(x+x) = sin(x)cos(x) + sin(x)cos(x) = sin(2x) = 2*sin(x)cos(x).

This means that there are two sin(x)cos(x). You can even write it as sin(2x) = 2cos(x)sin(x). Thus there is no second sin(x) haha.

It's not saying there is 2sin(x) and 1 cos(x). It is saying there is two sin(x)cos(x).

Hope this helps! :)

mes
Автор

thank you sir, sir can you help me with a question which says 1-2sintheta/costheta+sintheta is equal to costheta - sintheta how to prove that the left side is same at the right side

akagamishanks