jada741
07.05.2020 •
Mathematics
Rewrite the product as a sum: 10cos(5x)sin(10x)
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Ответ:
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)]
Ответ:
-3 (2y - 8) + 2y = 12
-6y + 24 + 2y = 12
-4y + 24 = 12
-4y = -12
y = 3
x = 2y - 8
x = 2(3) -8
x = 6-8
x = -2
Therefore, the coordinates are (-2, 3).