Write the expression as sine, cosine, or tangent of an angle.?

Can someone please walk me through the steps on how to write sin(9x)cos(x)-cos(9x)sin(x) as sine, cosine, or tangent? I'm doing a practice test so I really don't want just the answer, I want to actually know how to do it, I appreciate any help...

My answer choices are





2 Answers

  • Notice it resembles one of the sum-difference formulas.

    sin(a +/- b) = sin(a)cos(b) +/- cos(a)sin(b)

    which means...

    sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

    sin(a - b) = sin(a)cos(b) - cos(a)sin(b)


    a = 9x

    b = x

    sin(9x)cos(x) - cos(9x)sin(x) = sin(9x - x) = sin(8x)

  • http://www.sosmath.com/trig/Trig5/trig5/trig5.html

    The one you want is for the sum of two angles.

    Unfortunately---trig identities just have to be memorized. It takes too long to prove each one again during a test.

    If you want the proof of any particular one let me know thru comments and we can find it.

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