SOLUTION: Write cos(4𝑥) cos(3𝑥) − sin(4𝑥) sin(3𝑥) as a single trig function.

Question 1162367: Write cos(4𝑥) cos(3𝑥) − sin(4𝑥) sin(3𝑥) as a single trig function.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

Solve for cos():

Now (ignoring sin(4x)sin(3x) for the time being):

Which can be "simplified" to:

and further expanded to:

The part called "expression" must be zero since the left hand side is real, therefore:

EDIT: Fixed cos(4x) cut & paste error, it now reads properly

Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.

Use the basic argument addition formula for cosine cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) and you momentarily get cos(4x)*cos(3x) - sin(4x)*sin(3x) = cos(4x + 3x) = cos(7x). ANSWER

Solved.

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