How do you use the product to sum formulas to write $5 cos (- 5 β) cos 3 β$ $5cos(-5beta)cos3beta$ as a sum or difference?

Question

How do you use the product to sum formulas to write $5 cos (- 5 β) cos 3 β$ $5cos(-5beta)cos3beta$ as a sum or difference?

1 Answer

Impact of this question

2875 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-17T14:53:49

See below

Explanation:

Firstly, the sum of cosines is always written in the form $2 cos (\frac{P + Q}{2}) cos (\frac{P - Q}{2})$ $2cos(("P"+"Q")/2)cos(("P"-"Q")/2)$ , so we have to take the $5$ $5$ out.

$5 cos (- 5 β) cos 3 β = \frac{5}{2} (2 cos (- 5 β) cos 3 β)$ $5cos(-5beta)cos3beta=5/2(2cos(-5beta)cos3beta)$

Since $cos x$ $cosx$ is an even function, we know that $cos (- 5 β) = cos (5 β)$ $cos(-5beta)=cos(5beta)$

$\frac{5}{2} (2 cos (- 5 β) (3 β)) = \frac{5}{2} (2 cos 5 β cos 3 β)$ $5/2(2cos(-5beta)(3beta))=5/2(2cos5betacos3beta)$

Now it is trivial to find $P$ $"P"$ and $Q$ $"Q"$

$P = 5 β + 3 β = 8 β$ $"P"=5beta+3beta=8beta$

$Q = 5 β - 3 β = 2 β$ $"Q"=5beta-3beta=2beta$

$\frac{5}{2} (2 cos 5 β cos 3 β) = \frac{5}{2} (cos 8 β + cos 3 β)$ $5/2(2cos5betacos3beta)=5/2(cos8beta+cos3beta)$

Science

Math

Humanities

... and beyond

How do you use the product to sum formulas to write $5 cos (- 5 β) cos 3 β$ $5cos(-5beta)cos3beta$ as a sum or difference?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you use the product to sum formulas to write 5cos(−5β)cos3β5cos(-5beta)cos3beta as a sum or difference?

1 Answer

Explanation:

Related questions

Impact of this question

How do you use the product to sum formulas to write $5 cos (- 5 β) cos 3 β$ $5cos(-5beta)cos3beta$ as a sum or difference?