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3 years ago

Sin(A+B) - sin(A-B) = 2cos A sin BProve that answer please , I'm stuck

Mathematics

1 answer:

Mkey [24]3 years ago

7 0

Answer:

Step-by-step explanation:

Hello,

I assume that you know that

$sin(A+B)=sinAcosB+cosAsinB\\\\sin(A-B)=sinAcosB-cosAsinB$

One way to retrieve them quickly is to use Euler's formula and then,

$cos(A+B)+isin(A+B)=e^{i(A+B)}=e^{iA}e^{iB}=(cosA+isinA)(cosB+isinB)$

and you can replace B by -B for the second formula.

So, it comes that sin(A+B)-sin(A-B)=2cosAsinB

Hope this helps

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Which phrase can be represented by an equation? twice as much as a number 12 less than a number half of a number is 15 the diffe

jeka57 [31]

Answer:

Half of a number is 15

Step-by-step explanation:

First of all, add commas between each option so it's easier to read I had a hard time figuring out what the options were because of this.

An equation is a statement that the values of two mathematical expressions are equal. An expression is a collection of symbols that jointly express a quantity. This means there has to be an equal sign when the phrases are put into numerical form.

Twice as much as a number: 2X

12 less than a number: X - 12

Half of a number is 15: X/2 = 15

The difference of 20 and a number: 20 - X

As you can see, only one of these phrases is an equation by definition, and that is X/2 = 15, or half of a number is 15. That's because it's the only one that values two expressions as equal.

4 0

3 years ago

Read 2 more answers

Three trigonometric functions for a given angle are shown below. Sine theta = Negative StartFraction 77 Over 85 EndFraction, cos

Likurg_2 [28]

Trigonometric functions are the ratio of the different sides of a right-angled triangle. We can say that the coordinates of the point are (-77, 36).

<h3>What are trigonometric functions?</h3>

Trigonometric functions are the ratio of the different sides of a right-angled triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

$Sin(\theta) = \dfrac{-77}{85}$

$Cos(\theta) = \dfrac{36}{85}$

$Tan(\theta) = \dfrac{-77}{36}$

As we know that the Tangent(Tan) is the ratio of perpendicular and base. therefore, we can write the function as,

$\rm Tan(\theta) = \dfrac{Perpendicular}{Base} = \dfrac{-77}{36}$

therefore, the length of the perpendicular is 77, while the length of the base is 36.

As given to us that the value of sin is negative, therefore, the perpendicular will be on the negative side of the y-axis. While the value of cos is positive, therefore, the base will be on the positive side of the x-axis.

Thus, we can say that the coordinates of the point are (-77, 36).

Learn more about Trigonometric functions:

brainly.com/question/6904750

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2 years ago

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The length of a rectangle is four times its width.

melamori03 [73]

Answer:

200

Step-by-step explanation:

multiply the rectangle sides