+0  
 
+3
623
3
avatar

Write the product as a sum: 6sin(47y)cos(21y) =

Guest May 16, 2015

Best Answer 

 #1
avatar+537 
+13

sin(x+y)=sinx*cosy+cosx*siny

sin(x-y)=sinx*cosy-cosx*siny

so, sin(x+y)+sin(x-y)=sinx*cosy+cosx*siny+sinx*cosy-cosx*siny=2sinx*cosy

    sinx*cosy=1/2[sin(x+y)+sin(x-y)]

orginal qustion=6*sin(47y)*cos(21y)=(1/2)*6*[sin(47y+21y)+sin(47y-21y)=3*[sin68y+sin26y]

                     =3sin68y+3sin26y

fiora  May 16, 2015
 #1
avatar+537 
+13
Best Answer

sin(x+y)=sinx*cosy+cosx*siny

sin(x-y)=sinx*cosy-cosx*siny

so, sin(x+y)+sin(x-y)=sinx*cosy+cosx*siny+sinx*cosy-cosx*siny=2sinx*cosy

    sinx*cosy=1/2[sin(x+y)+sin(x-y)]

orginal qustion=6*sin(47y)*cos(21y)=(1/2)*6*[sin(47y+21y)+sin(47y-21y)=3*[sin68y+sin26y]

                     =3sin68y+3sin26y

fiora  May 16, 2015
 #2
avatar+89865 
0

Very nicely done,  fiora.......!!!  Impressive....

 

 

CPhill  May 16, 2015
 #3
avatar+20024 
+10

Write the product as a sum: 6sin(47y)cos(21y) = ?

 

$$\boxed{
\small{\text{
Formula:
$
\begin{array}{rcl}
\sin u+\sin v=2\sin \frac{u+v}{2}\cos \frac{u-v}{2}
\end{array}
$}}
}$$

$$\small{\text{$
\begin{array}{rcl}
47y = \dfrac{u+v}{2} \qquad 21y=\dfrac{u-v}{2}\\\\
u=\dfrac{u+v}{2}+\dfrac{u-v}{2}=47y+21y=68y\\\\
v=\dfrac{u+v}{2}-\dfrac{u-v}{2}=47y-21y=26y\\\\
\end{array}
$}}$$

 

$$\small{\text{$
\begin{array}{rcl}
\sin u+\sin v&=&2\sin \frac{u+v}{2}\cos \frac{u-v}{2}\\\\
\sin {(68y)}+\sin {(26y)} &=&2\sin{( 47y )}\cos{( 21y )} \quad | \quad \cdot 3 \\\\
3\sin {(68y)}+3\sin {(26y)} &=&6\sin{( 47y )}\cos{( 21y )}
\end{array}
$}}$$

heureka  May 16, 2015

34 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.