Verify the identity.sin(x + y) cos(x - y) = sin x cos x + cos y sin y

What will be an ideal response?


sin(x + y) cos(x - y) = [sin x cos y + cos x sin y][cos x cos y + sin x sin y]
 = sin x cos x cos2 y + cos y sin y sin2 x + sin y cos y cos2 x + cos x sin x sin2 y
  = sin x cos x(cos2 y + sin2 y) + cos y sin y(sin2 x + cos2 x)
 = sin x cos x + cos y sin y

Mathematics

You might also like to view...

Solve the problem.Find the sum of the first 10 terms of the arithmetic sequence 88, 159, 230, . . . .

A. -3635 B. 4075 C. -2315 D. 3635

Mathematics

A bakery makes sweet rolls and donuts. A batch of sweet rolls requires  of flour,  eggs, and  of sugar. A batch of donuts requires  of flour,  eggs, and 

alt="" style="vertical-align: -4.0px;" /> of sugar. Set up an initial simplex tableau to maximize profit.The bakery has 580 lb of flour, 660 dozen eggs,  of sugar. The profit on a batch of sweet rolls is  and on a batch of donuts is $62.00.

A.
  

B.  
  

C.
 

D.  
 

Mathematics

Without graphing the function, determine its amplitude or period as requested.y = -4 sin 5xFind the amplitude.

A.
B.
C. 4
D.

Mathematics

The pictograph shows the number of bicyclists who participated in the Labor Day weekend bicycle race for the years indicated. In what year did the least number of cyclists participate?

A. 2003 B. 2004 C. 2005 D. 2007

Mathematics