Convert products to sum or difference

Question

a) 2sinα•cos2α

b) 2cos3α•cos2α

Answer 1

We can  use this formula

sin(x)cos(y)= 1/2 [sin(x+y)+sin(x−y)]

 

a) 2sin(α)•cos(2α)= 2*(1/2)[sin(α+2α)+sin(α-2α)] =sin(3α)-sin(α).

[ Note that sin(-x)=-sin(x)]

 

b)Here we use

cos(x)cos(y)= 1/2 [cos(x−y)+cos(x+y)]

 

2cos3α•cos2α=2(1/2)[cos(3α-2α)+cos(3α+2α)]=cos(α)+cos(5α).