+0  
 
+1
72
2
avatar+91 

Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine.

 

4 sin^4 2x

 Dec 1, 2018
 #1
avatar+3613 
0

if you can figure the last one out you can figure this one out

 Dec 1, 2018
 #2
avatar+94545 
+1

4 sin^4 (2x)   

 

[2sin^2 (2x)]^2  =

 

4 [sin^2(2x)]^2  =

 

4 [ (1 - cos (4x) ) / 2 ]^2 =

 

 [ 1 - cos (4x) ] ^2 =

 

1 - 2cos(4x) + cos^2(4x) =

 

1 - 2cos(4x) +  [ 1 - cos (8x)] / 2   =

 

1 - 2 cos (4x) + (1/2) - (1/2)cos(8x)     =

 

(1/2) [ 2 - 4cos(4x) + 1 - cos(8x) ]  =

 

(1/2)  [ 3 - 4cos(4x) - cos(8x)  ]

 

 

cool cool cool

 Dec 1, 2018

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