Express sin 3x sin 7x as a sum or difference
To express sin 3x sin 7x as a sum or difference, we can use the product-to-sum identity.
The product-to-sum identity states that sin A sin B can be expressed as (1/2) * [cos(A - B) - cos(A + B)].
In this case, let A = 3x and B = 7x.
So, sin 3x sin 7x can be expressed as
(1/2) * [cos(3x - 7x) - cos(3x + 7x)]
Simplifying, we have
(1/2) * [cos(-4x) - cos(10x)]
Now, we can express this as a sum or difference.
Using the identity cos(-x) = cos(x), we have
(1/2) * [cos(4x) - cos(10x)]
Therefore, sin 3x sin 7x can be expressed as a difference:
(1/2) * [cos(4x) - cos(10x)]
To express sin(3x) sin(7x) as a sum or difference, we can use the trigonometric identity:
sin(A) sin(B) = (1/2) [ cos(A - B) - cos(A + B) ]
In this case, A = 3x and B = 7x. Plugging these values into the identity, we get:
sin(3x) sin(7x) = (1/2) [ cos(3x - 7x) - cos(3x + 7x) ]
Simplifying further:
sin(3x) sin(7x) = (1/2) [ cos(-4x) - cos(10x) ]
Finally, we can write sin(3x) sin(7x) as a sum or difference:
sin(3x) sin(7x) = (1/2) [ cos(4x) - cos(10x) ]