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BabaBlast [244]
1 year ago
6

How do I verify this identity? I know you should write sin2a as sin(a+a).

Mathematics
1 answer:
Kisachek [45]1 year ago
7 0

SOLUTION

Given the question in the image, the following are the solution steps to verify the identity

STEP 1: Write the given identity

\sin 2\alpha=2\sin \alpha\cos \alpha

STEP 2: Verify the identity

\begin{gathered} \sin 2\alpha=2\sin \alpha\cos \alpha \\ \text{Consider the left hand side of the above trigonometry identity.} \\ \text{That is, }\sin 2\alpha\text{.} \\ \text{ Rewrite }\sin 2\alpha\text{ as }\sin (\alpha+a) \\ \text{ It is known that }\sin (a+b)=\sin (a)\cos b+\cos (a)\sin (b) \\ U\sin g\text{ this statement above, we have;} \\ \sin (\alpha+a)=\sin a\cos \alpha+\cos a\sin \alpha \\ \text{It is known that }xy+yx=xy+xy=2\times xy=2xy \\ U\sin g\text{ this statement above, we have;} \\ \sin a\cos \alpha+\cos a\sin \alpha=\sin a\cos \alpha+\sin \alpha\cos \alpha=2\times\sin \alpha\cos \alpha=2\sin \alpha\cos \alpha \\ \text{Hence, }\sin 2\alpha=2\sin \alpha\cos \alpha \end{gathered}

The verification of the identity is as seen above.

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NEED HELP ASAPPP!!! Drag each scenario to show whether the final result will be greater than the original
Lemur [1.5K]

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value =x+30-30=x, it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value =x-\dfrac{20}{100}x=x-0.2x=0.8x

Afer 40% increase.

New value =0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x, it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value =x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x, it is same as original value.

4. A 75% increase followed by a 33% decrease

New value =x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x, it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value =x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x, it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

6 0
3 years ago
You made Marcellus 3 times as tall as Dan but you dragged Marcellus’s mouth to be 5.46 times as wide as Dan’s mouth. A proportio
garri49 [273]

Answer:

22.34 cm wide

Step-by-step explanation:

7 0
3 years ago
Find a second-degree polynomial (that is, an equation of the form y =a + bx + cx2 d that goes through the three points (0, 1), (
Lostsunrise [7]

Answer:

y = 1 - x^2

Step-by-step explanation:

we're given three points (0,1),(1,0) and (-1,0). and and equation of a parabola

y = a + bx + cx^2

we can plug in each of the coordinates, and 3 equations

(x,y) = (0,1)

1 = a + b(0) + c(0)^2

a=1\quad\quad\Rightarrow A

(x,y) = (1,0)

0 = a + b(1) + c(1)^2

a + b + c=0\quad\quad\Rightarrow B

(x,y) = (-1,0)

0 = a + b(-1) + c(-1)^2

a - b + c=0\quad\quad\Rightarrow C

These are are three equations, well we can simultaneously solve them to find the values of a, b and c.

we already found that, a = 1. so we plug this value in the rest of the equations. we'll use equation B.

a + b + c=0

1 + b + c=0

b=-1-c

we can substitute this value of b and a = 1, equation C

a - b + c=0

1 -(-1-c) + c=0

1 +1+c + c=0

2+2c=0

c=-1

we can use this value of c back in b

b=-1-(-1)

b=0

hence our equation of the 2-degree polynomial will be:

y = a + bx + cx^2

y = 1 + (0)x + (-1)x^2

y = 1 - x^2

and this polynomial indeed passes through all the points (0, 1), (1, 0), and (-1, 0).

And since these are the only solutions to the simultaneous equation we solved (i.e. we have single values of a,b and c). there's no other possibility.

8 0
3 years ago
If LM = 22 and MN = 15, find LN.
Bas_tet [7]

Answer:

LN=37 units

Step-by-step explanation:

In this problem I will assume that M is a point between point L and point N

therefore

LN=LM+MN

substitute the given values

LN=22+15=37 units

5 0
3 years ago
Find the x <br> Please help me and show how you got it :)
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9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The parallel lines divide the sides proportionally, so ratios of corresponding sides are the same.

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Multiplying by 105, we have ...

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  7x +35 = 15x +3 . . . . . eliminate parentheses

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  4 = x . . . . . . . . divide by 8

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