1 - cos2x + cos3x - cos5x; sin(a) - sin(b) - sin(c)

[truth_seeker]

1) Put in the form of product or of a quotient of sine or cosine:

. . .1 - cos2x + cos3x - cos5x

2) If a + b + c = pi, then put "sin(a) - sin(b) - sin(c)" in the form of a product.

I have probable answers in mind, but I want to check them and be sure!

Thanks in advance!

 

[stapel]

I have probable answers in mind, but I want to check them and be sure!

The tutors will be glad to look over your work and check your solutions, but you'll need to post that information first.

Thank you.

Eliz.

 

[truth_seeker]

no, please gimme help in solving it!!!
what are the stepsi should follow?
i really need this! it's urgent!!!

 

[stapel]

Then why did you say you had solutions...? :?

1) Your formatting is ambiguous. Do you mean either of the following?

. . . . .1 - cos²(x) + cos³(x) - cos⁵(x)

. . . . .1 - cos(2x) + cos(3x) - cos(5x)

What have you tried? Where are you stuck?

2) There are probably many ways to proceed on this, and there may be more than one answer. ("A product" isn't very specific.) One way to start might be to use "pi = a + b + c" to substitute for one of the arguments. Then use trig identities to expand the expression.

What have you tried? Where are you stuck?

Please be specific. Thank you.

Eliz.

 

[truth_seeker]

Then why did you say you had solutions...? :?

1) Your formatting is ambiguous. Do you mean either of the following?

. . . . .1 - cos²(x) + cos³(x) - cos⁵(x)

. . . . .1 - cos(2x) + cos(3x) - cos(5x)

What have you tried? Where are you stuck?

2) There are probably many ways to proceed on this, and there may be more than one answer. ("A product" isn't very specific.) One way to start might be to use "pi = a + b + c" to substitute for one of the arguments. Then use trig identities to expand the expression.

What have you tried? Where are you stuck?

Please be specific. Thank you.

Eliz.

for number 1:1 - cos(2x) + cos(3x) - cos(5x)
1 - cos(2x)=2sin²x
cos(3x) - cos(5x) =-2(sin( (3x-5x)/2) ).(sin(3x+5x)/2) )
then simplify, and factorize
and reach the final answer : 4sin(x)( sin(5x/2)cos(3x/2) )
am i right?

for number 2, i guess i have to use something like a+b=pi-c ==>sin(a+b)=-sin(c)
and then continue onwards....but i have no idea

reply fast please

 

[truth_seeker]

i was able to solve these & the answers checked out.

thanx giyz 4 ur help!