PLEASE SHOW ALL OF YOUR WORK

Question

sin(6x)-sin(3x)

this can be written as a product of sin or cosine

Answer 1

Hi,

When ask you change to product it means you need to have only product

sin(6x)-sin(3x)

you need to know this formula: sin a - sin b = 2 sin ( a - b )/2 * cos ( a + b )/2

now replace given information to this property

sin(6x)-sin(3x) = 2 sin ( 6x - 3x ) / 2 cos ( 6x + 3x )/2

= 2 sin 3/2 x * cos 9/2 x

you see, your answer is ONLY product

I hope it was useful,

Minoo

Answer 2

sin(6x) - sin(3x)

= 2sin(3x)cos(3x) - sin(3x)

=sin(3x)((2cos(3x)- 1))