Question

Which expression is equivalent to sin(1.8x) sin(0.5x)? 0.5[sin(2.3x) + sin(1.3x)] 0.5[sin(2.3x) − sin(1.3x)] 0.5[cos(1.3x) − cos(2.3x)] 0.5[cos(2.3x) − cos(1.3x)]?

Answer 1

In trigonometry which relates the sides and angles of the triangle, there is an identity which states that,
                     (sinA)(sinB) = 0.5(cos (A -B) - cos (A + B))
In this item, our A and B are 1.8x and 0.5x, respectively. 

Substituting,
                   sin(1.8x)sin(0.5x) = 0.5(cos (1.8x - 0.5x) - cos(1.8x + 0.5x))
                   sin(1.8x)sin(0.5x) = 0.5(cos 1.3x - cos 2.3 x)