Question

a)Write cos3x-cosx as a product.
b) rewrite sin4(x/2) in terms of the first power of the cosine.

Answer 1

whatever the answer, I don't have time to write trigs. do you still have trouble doing it?

Answer 2

yes

Answer 3

use these equations:

cos(a+b)=cos(a)cos(b) - sin(a)sin(b)
cos(a-b)=cos(a)cos(b) + sin(a)sin(b)

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Do you still want a more hint?

Answer 4

Adding them up, you'll get

cos(a)cos(b)=1/2[cos(a+b) + cos(a-b)]

OK????????????????????????????????????????????????????

Answer 5

k

Answer 6

No No sorry. It was for sth else... you this

sin(ax)sin(bx)=1/2[cos(a-b)x - cos(a+b)x]

then

cos(a-b)x - cos(a+b)x = 2sin(ax)sin(bx)

to obtain a and b, solve these two equations:

a-b=3
a+b=1

a=2
b=-1

so you get

cos(3x)-cos(x)=2sin(2x)sin(-x)=-2sin(2x)sin(x)

OK????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Answer 7

mhm..

Answer 8

Made sense????

Answer 9

kinda..i'll figure it out tho

Answer 10

thanks..

Answer 11

No problem :)