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?

1 Answer
Nghi N.
Aug 28, 2015

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)

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