rewrite the product as a sum: 10cos(5x)sin(10x)

Question

rewrite the product as a sum: 10cos(5x)sin(10x)

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Skylar 2 months 2021-10-13T15:11:10+00:00 1 Answer 0 views 0

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    2021-10-13T15:12:51+00:00

    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 have

    10cos(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) = -sinx

    Thus 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)]

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