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1 year ago

Subtract the sum and difference identities for sin x to derive 1/2 [sin(x+y)+sin(x-y)]= cos x sin y

Mathematics

1 answer:

inessss [21]1 year ago

6 0

The required trigonometric identity is 1/2[sin(x + y) - sin(x - y)] = cosxsiny

To answer the question, we need to know what trigonometric identities are

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

Trigonometric identities are relationships between the trigonometic ratios.

Since we require cosxsiny

Given that

sin(x + y) = sinxcosy + cosxsiny and
sin(x - y) = sinxcosy - cosxsiny

So, subtracting both expressions, we have

sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy - cosxsiny)

= sinxcosy + cosxsiny - sinxcosy + cosxsiny

= sinxcosy - sinxcosy + cosxsiny + cosxsiny

= 0 + 2cosxsiny

= 2cosxsiny

sin(x + y) - sin(x - y) = 2cosxsiny

Dividing through by 2, we have

1/2[sin(x + y) - sin(x - y)] = cosxsiny

So, the required trigonometric identity is 1/2[sin(x + y) - sin(x - y)] = cosxsiny

Learn more about trigonometric identities here:

brainly.com/question/26609988

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Lyrx [107]

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As we get closer to x=-3, the limit is approaches -1, on both sides of -3 so this is a good limit so c is 8.

Step-by-step explanation:

In order for a limit to exists, the left side limit must exist and right side limit must exist and on top of that, they must be equal to each other.

In this case, this a piece wise function and by definition of a limit that exist, the limit of this piece wise function as x approaches 3 from either side, must be equal.

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2 years ago

What is the equation of the graph below? A graph shows a parabola that opens up and crosses the x axis at negative two and negat

Anastaziya [24]

Answer:

$y=(x+3)^{2} -1$

Step-by-step explanation:

General equation of a parabola that opens up is $y=a(x-h)^{2} +k$ , a>0

So equation becomes $y=(x-h)^{2} +k$ which implies option A and option B can never be true for this parabola.

Also this parabola's vertex lies in 3rd quadrant where coordinates of both x and y will be negative.

So, the equation of parabola will be of the form $y=(x+h)^{2} - k$

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2 years ago

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PLEASE HELP!!!!! DUE TODAY!!!!!

prisoha [69]

Answer:

12.4 cm³

Step-by-step explanation:

From the picture attached,

Radius of the circular top of the cone = $\frac{\text{Diameter}}{2}$ = $\frac{2}{2}=1$

Height of the cone = h

Lateral height of the cone = h

By applying Pythagoras theorem in the right triangle of the cone,

l² = r² + h²

6² = 1² + h²

h = $\sqrt{36-1}$

h = $\sqrt{35}$

Ice cream needed to fill one cone = Volume of the cone

Since, formula for the volume of the cone V = $\frac{1}{3} \pi r^{2} h$

V = $\frac{1}{3}\pi (1)^2(\sqrt{35})$

= 6.195

≈ 6.20 cm³

Ice cream needed to fill the two cones = 2 × 6.20

= 12.4 cm³

Therefore, ice cream needed to fill the two cone = 12.4 cm³

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2 years ago