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3 years ago

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

Mathematics

1 answer:

mote1985 [20]3 years ago

8 0

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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ExtremeBDS [4]

Given:

Consider the below figure attached with this question.

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