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Gemiola [76]
3 years ago
9

8x-3=15x+18 a. x=-3 b. x=3 c. x=2.1 d. x=0.9

Mathematics
1 answer:
natka813 [3]3 years ago
6 0
8x - 3 = 15x + 18

First, subtract 8x from both sides. / Your problem should look like: -3 = 15x + 18 - 8x
Second, simplify 15x + 18 - 8x to 7x + 18. / Your problem should look like: -3 = 7x + 18
Third, subtract 18 from both sides. / Your problem should look like: -3 - 18 = 7x
Fourth, subtract -3 - 18 to get -21. / Your problem should look like: -21 = 7x
Fifth, divide both sides by 7. / Your problem should look like:-\frac{21}{7} = x
Sixth, simplify \frac{21}{7} to 3. / Your problem should look like: -3 = x
Seventh, switch sides. / Your problem should look like: x = -3

Answer: x = -3

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Given the trigonometry expression:

sin 3x = sin(2x+x),

In trigonometry identity;

Sin(A+B) = sinAcosB + cosAsinB

The expression above will then become;

sin(2x+x) =sin2xcosx+cos2xsinx\\sin(2x+x) =2sinxcosxcosx + (1-2sin^2x)sinx\\sin(2x+x) =2sinxcos^2x + (1-2sin^2x)sinx\\

Recall that sin^2x + cos^x = 1, hence;

sin(2x+x) =2sinx(1-sin^2x)+ (1-2sin^2x)sinx\\Expand\\sin(2x+x) =2sinx-2sin^3x+ sinx-2sin^3x\\sin(2x+x) =2sinx + sinx-2sin^3x-2sin^3x\\sisn(2x+x) = 3sinx-4sin^3x

This shows that sin3x =3sinx-4sin^3x (Proved!)

Learn more here: brainly.com/question/7331447

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