Welcome to our community

Be a part of something great, join today!

Trigonometry Trig Expression simplification

Cbarker1

Active member
Jan 8, 2013
241
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?
 
Last edited:

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,680
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

Active member
Jan 8, 2013
241
I wished to use sum-product identity.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
With differing coefficients on the cosine terms, I don't see how you can use a sum-to-product identity.