How do you simplify sin2x×sin7x?

1 Answer
Dec 1, 2016

Use the exponential form of the trigonometric functions:

sin(7x)=e7ixe7ix2i

sin(2x)=e2ixe2ix2i

sin(2x)sin(7x)=e7ixe7ix2ie2ixe2ix2i=

=e9ixe5ixe5ix+e9ix(2i)2=e5ix+e5ix4e9ix+e9ix4

sin(2x)sin(7x)=cos(5x)cos(9x)2