MHB Trig Expression simplification

[cbarker1]

What identity I need to use for simplifying this trig expression into one expression?$cos(3x)+4hcos(x)$ where h is a constant.

Thank you for your help.

Can you explain, too?

 

[anemone]

To simplify an expression that contains two terms means we need to combine these two terms to become one single term, i.e. by factoring out the common factor.

In our case ($\cos3x+4h \cos x$), we need to express $\cos 3x$ in terms of $\cos x$ since the second term has a $\cos x$ in it.

By using the triple-angle formula for $ \cos 3x$, where $ \cos 3x=4\cos^3x-3 \cos x$, we can simplify the original expression as follows:

$\displaystyle \cos3x+4h \cos x =(4\cos^3x-3 \cos x)+4h \cos x=\cos x(4\cos^2x-3+4h)$

 

[cbarker1]

I wished to use sum-product identity.

 

[MarkFL]

With differing coefficients on the cosine terms, I don't see how you can use a sum-to-product identity.