Question

Write the following sums or differences as a product (a)sin 2x + sin 3x (b)cos 5x- cos 3x (c)sin 4x -sin 2x (d)cos 3x + cos 6x?

Answer 1

Convert trig expressions into products

Explanation:

Reminder of sum and differences trig identities:
`sin a + sin b = 2 sin ((a + b)/2).cos ((a - b)/2)`
`sin a - sin b = 2cos ((a + b)/2).sin ((a - b)/2)`
`cos a + cos b = 2cos ((a + b)/2).cos ((a - b)/2)`
`cos a - cos b = - 2sin((a + b)/2)sin ((a - b)/2)`
Answers:
a. `sin 2x + sin 3x = 2sin((5x)/2).cos (x/2)`
b. `sin 4x - sin 2x = 2cos (3x).sin x`
c. `cos 5x - cos 3x = - 2sin (4x).sin x`
d. `cos 3x + cos 6x = 2cos ((9x)/2) .cos ((3x)/2)`