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

1 Answer
Nghi N.
Jun 15, 2018

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))#

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