Question

Use the product-to-sum formulas to rewrite the product as a sum or difference. 9 cos(−9β) sin 5β?

Answer 1

Note:
`cos (-9b) = cos 9b`
`sin (5b) = cos (pi/2 - 5b)`
Trig identity:
`cos a.cos b = 1/2[cos ((a - b)/2) + cos ((a + b)/2)]`
We get in this case:
`f(b) = 9cos (9b).sin (5b) = 9cos (9b).cos (pi/2 - 5b)`
`(a - b)/2 = 7b - pi/4`
`(a + b)/2 = 2b + pi/4`
`f(b) = (9/2)(cos (7b - pi/4)) + (9/2)(cos (2b + pi/4))`