Use Euler’s formula for exp(ix) and exp(-ix) to write cos(x) as a combination of exp(ix) and exp(-ix)

Answer = (cos(x) = (exp(ix)+exp(-ix))/2)

For real a and b, use the previous answer to find write both cos(a+b) and cos(a)cos(b) in terms of exp. Throughout the rest you will probably use exp(x+y)=exp(x)exp(y).

Step-by-step explanation:

We need to expand cos(a+b) using the cos addition formula.

We know that we also need to use Euler's formula for sin, which is:

(you can get this from a similar way of getting the first result, of simply just expanding and seeing the necessary result)

We can now substitute our cos's and sin's for e's

Now lets multiply out both of our terms, I'm using the exponent multiplication identity here ()

Now we can subtract these two terms.

This is starting to look a lot tidier, let's cancel the 2

mx+89b(-98)nb

step-by-step explanation: