Answer:
Explanation:
a. To write the product a.sin(3x)cos(2x) as a sum, we can use the identity:
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
Using this identity, we can write:
a.sin(3x)cos(2x) = a.sin(3x)cos(x + x)
= a[sin(3x)cos(x) + cos(3x)sin(x)]
= a[sin(x)cos(3x) + sin(3x)cos(x)]
= a.sin(x)(cos(3x) + sin(3x))
Therefore, the product a.sin(3x)cos(2x) can be written as the sum a.sin(x)(cos(3x) + sin(3x)).
b. To write the product cos(7x)cos(2x) as a sum, we can use the identity:
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Using this identity, we can write:
cos(7x)cos(2x) = cos(7x)cos(-x - (-x + 2x))
= cos(7x)cos(-x)cos(-(-x+2x)) - sin(7x)sin(-x)cos(-(-x+2x))
= cos(7x)cos(x)cos(x) + sin(7x)sin(x)sin(x)
= cos(7x)cos^2(x) + sin(7x)sin^2(x)
Therefore, the product cos(7x)cos(2x) can be written as the sum cos(7x)cos^2(x) + sin(7x)sin^2(x).