sinx cosx(x+y) - cosx sin(x+y)?

Question

how do u do this i need help plzz :(

can u show work on how you get the answer too plz :)

Rajkiran how did u get step 2 and 3 ?

Answer 1

You need the formulas:
cos(x + y) = cos x * cos y - sin x * sin y
sin(x + y) = sin x * cos y + cos x * sin y

therefore, the above expression is
sin x * ( cos x * cos y - sin x * sin y ) - cos x *(sin x * cos y + cos x * sin y) =
sin x * cos x * cos y - sin x * sin x * sin y - cos x * sin x * cos y - cos x * cos x * siny = - sin y

Answer 2

sinx cosx(x+y) - cosx sin(x+y) = sin[x - (x+y)] = sin(-y) = -siny

Answer 3

Here's some checks of proof ( Click back then go on http://www.uutx.com to get started)

Answer 4

If by this you mean

(sin(x) * cos(x + y)) - (cos(x) * sin(x + y))

(sin(x) * (cos(x)cos(y) - sin(x)sin(y))) - (cos(x) * (sin(x)cos(y) + cos(x)sin(y)))

sin(x)cos(x)cos(y) - sin(y)sin(x)^2 - sin(x)cos(x)cos(y) - sin(y)cos(x)^2

(1 - 1)sin(x)cos(x)cos(y) - sin(y)sin(x)^2 - sin(y)cos(x)^2

(-sin(y))(sin(x)^2 + cos(x)^2)

(-sin(y))(1)

ANS : -sin(y)

Answer 5

Sin(x)Cos(x+y)-Cox(x)Sin(x+y)
=sin(x)(Cos(x)Cos(y)-Sin(x)Sin(y))
-cos(x)(Sin(x)Cos(y)+Cos(x)Sin(y))
=sin(x)Cos(x)Cos(y) - Sin(x)Sin(x)Sin(y) - Cos(x)Sin(x)Cos(y)
- Cos(x)Cos(x)Sin(y)
=-Sin(y)((Cos(x))^2 + (Sin(x))^2)
=-Sin(y)

Answer 6

I actually forgot how to do this. Can you believe me.

Answer 7

sin[x-(x+y)]
=sin(-y)
=-siny