Jonathan T.

asked • 12/01/16

simplify the expression (sinAsinB)(cosAcosB)

simply simplify the expression. i have to find out if my answer i have is right or wrong

1 Expert Answer

By:

Inactive Tutor answered • 12/01/16

Tutor
New to Wyzant

See tutors like this
See tutors like this
sinAsinB + cosAcosB = cos(A - B) is this what you want?
Upvote • 0 Downvote
More
Report

Jonathan T.

thats what i have. what i got is SinA-SinB. 
 
i did it like this:
(SinA-SinB)(cosAcosB)
=sinAcosA+sinAcosB-sinBcosA-sinBcosB
=sinAcosA-sinBcosB, then i used product to sum identity and got
=1/2(sin(A+A) + sin(A-A)) - 1/2(sin(B+B) + sin(B-B))
=1/2sin(2a) - 1/2sin(2B)
=sinAsinB.
i feel like i may have gone wrong with either foiling it or doing the product to sum identity. 
Report

12/01/16

Inactive Tutor

The first line of your solution is different that the product in the posting.
Report

12/01/16

Jonathan T.

you are absolute correct. sorry about that.
Report

12/01/16

Inactive Tutor

The second line should only be a binomial unless the second parenthesis contains a minus sign.
Report

12/01/16

Jonathan T.

i wrote it wrong again. the problem is (sinA-sinB)(cosA+cosB)
Report

12/01/16

Inactive Tutor

How did line 2 collapse to line 3?
Report

12/01/16

Jonathan T.

i guess thats where i went wrong. any idea what i did wrong ther?
Report

12/01/16

Inactive Tutor

sinAcosA + sinAcosB - sinBcosA - sinBcosB
sinAcosB - sinBcosA + sinAcosB - sinBcosA   commute
sin(A - B) + sin(A - B)                                 difference formula
2sin(A - B)
 
Report

12/01/16

Jonathan T.

where does the SinAcosA and -SinBcosB go?
Report

12/04/16

Jonathan T.

or is (SinAcosB)-(SinBcosA) the same as (SinACosA-sinBcosB)
Report

12/04/16

Inactive Tutor

My error
sinAcosA + sinAcosB - sinBcosA - sinBcosB
sinAcosB - sinBcosA + sinAcosA - sinB cosB   communite
sin(A - B) + sinAcosA - sinBcosB                   difference formula
Report

12/05/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.