SOLUTION: Derive at least the three (3) equivalent expressions of the trigonometric expression sin 2theta using the sum/difference identities .

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Question 607261: Derive at least the three (3) equivalent expressions of the trigonometric expression sin 2theta using the sum/difference identities .

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
All you have to do is
  • Figure out sums and/or differences that result in 2x
  • Rewrite {{sin(2*theta)}}} as the sin(a sum) or sin(a difference)
  • And then apply the appropriate identity.

There are literally an infinite number of ways to express 2x as a sum or difference:
x+x
9x + (-7x)
0.4x + 0.6x
3x-x
14000x - 13998x
etc.

Using sin(A+B) = sin(A)cos(B) + cos(A)sin(B) for the sums and sin(A-B) = sin(A)cos(B) - cos(A)sin(B) for the differences we get:
sin(2x) = sin(x+x) = sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x) (Surprised?)
sin(2x) = sin(9x +(-7x)) = sin(9x)cos(-7x) + cos(9x)sin(-7x)
sin(2x) = sin(0.4)x + 0,6x) = sin(0.4x)cos(0.6x) + cos(0.4x)sin(0.6x)
sin(2x) = sin(3x-x) = sin(3x)cos(x) - cos(3x)sin(x)
sin(2x) = sin(14000x - 13998x) = sin(14000x)cos(13998x) - cos(14000x)sin(13998x)

See if you can figure out some of your own!