Homework Help

Examine if equation sin(x-y)cosx-sinx cos(x-y) can be simplifyed?

user profile pic

minlux | Honors

Posted July 30, 2013 at 11:18 AM via web

dislike 1 like

Examine if equation sin(x-y)cosx-sinx cos(x-y) can be simplifyed?

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 30, 2013 at 11:37 AM (Answer #1)

dislike 1 like

The given expression represents the expansion of the following trigonometric difference identity, such that:

`sin (theta - beta) = sin theta*cos beta - sin beta*cos theta`

Replacing `x - y` for `theta` and `x` for `beta` , yields:

`sin (x - y)*cos x - sin x*cos (x - y) = sin (x - y - x)`

Reducing duplicate angles, yields:

`sin (x - y)*cos x - sin x*cos (x - y) = sin(-y)`

By definition, `sin(-y) = -sin y` , hence, replacing `- sin y` for `sin(-y)` , yields:

`sin (x - y)*cos x - sin x*cos (x - y) = - sin y`

Hence, reducing the given trigonometric expression, yields `sin (x - y)*cos x - sin x*cos (x - y) = - sin y.`

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes