rewrite the product as a sum: 10cos(5x)sin(10x) Question rewrite the product as a sum: 10cos(5x)sin(10x) in progress 0 Math Skylar 2 months 2021-10-13T15:11:10+00:00 2021-10-13T15:11:10+00:00 1 Answer 0 views 0

## Answers ( )

Answer:10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]Step-by-step explanation:In this question, we are tasked with writing the product as a sum.To do this, we shall be using the sum to product formula below;

cosαsinβ = 1/2[ sin(α + β) – sin(α – β)]From the question, we can say α= 5x and β= 10x

Plugging these values into the equation, we have10cos(5x)sin(10x) = (10) × 1/2[sin (5x + 10x) – sin(5x – 10x)]= 5[sin (15x) – sin (-5x)]We apply odd identity i.e sin(-x) = -sinxThus applying same to sin(-5x)

sin(-5x) = -sin(5x)Thus;5[sin (15x) – sin (-5x)] = 5[sin (15x) -(-sin(5x))]= 5[sin (15x) + sin (5x)]Hence, 10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]