How Do You Express sin(7t) - sin(6t) Using Trig Identities?

AI Thread Summary
To express sin(7t) - sin(6t) as a product of two trigonometric functions, the relevant identity for the difference of sines can be applied. The identity states that sin(A) - sin(B) = 2cos((A+B)/2)sin((A-B)/2). By substituting A with 7t and B with 6t, the expression can be simplified to 2cos((13t)/2)sin((t)/2). Some participants in the discussion struggled with the approach, indicating a need for clarity on applying trigonometric identities effectively. Utilizing the correct identity allows for a straightforward transformation of the expression.
Thadis
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Homework Statement


Write sin(7t)-sin(6t) as a product of two trig. functions.


Homework Equations


e^(ix)=cos(x)+isin(x)
sin(2x)=2cos(x)sin(x)
cos(2x)=cos^2(x)-sin^2(x)


The Attempt at a Solution



I do not really know how to approach this. I have tried using the sin(2x) identity but I could not get the correct answer from it. Can anyone help?
 
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Thadis said:

Homework Statement


Write sin(7t)-sin(6t) as a product of two trig. functions.


Homework Equations


e^(ix)=cos(x)+isin(x)
sin(2x)=2cos(x)sin(x)
cos(2x)=cos^2(x)-sin^2(x)


The Attempt at a Solution



I do not really know how to approach this. I have tried using the sin(2x) identity but I could not get the correct answer from it. Can anyone help?

There is a trig identity for sin(A)-sin(B). You can either look it up or work it out by figuring out what sin(a+b)-sin(a-b) would be using the addition formulas.
 

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